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Does your school have a strange schedule/lots of free periods? You seem to be able to get to a computer at all times of the day, I've been curious how you manage that with school/homework.

HAHAHAHAHAHAHA! Yes, I have no life, and yes, except today, I spend roughly 2 hours on Brilliant. Which is tough because I'm preparing for a Bar-Mitzvah and I'm swimming. So yeah. I am a Brilliantic for life.

Nice, it's pretty funny how you said you had no life, my friends tell me that all the time and make fun of me for getting on this website a lot. There all like, " oh ya Robert, your website is only for brilliant people. In a stupid sarcastic tone. Didn't know you were Jewish, that's pretty cool! What's your plan for your Bar-Mitzvah. My friend went to a nice hotel in Mexico and ate a ton of food. He said it was pretty freaking amazing.

@Robert Fritz
–
The service is gonna be pretty regular, with a frickin wild party after. For my B'nai-mitzvah, or "good deed", I'm tutoring a bunch of 5th graders about MATHCOUNTS and problem-solving techniques so that they're prepared to be on the MATHCOUNTS team in middle school. It's frickin boss, dude. :D

@Finn Hulse
–
Sweet! I also have to ask, have you ever tried science bowl. I'm stuck between doing track, science bowl, or mathcounts . Plus I just found out that for the science and math competitions that my magnet school can't compete in them as a team I was like, " what the **!" Luckily, I heard my other school actually has a decent team. I guess I'll try it next year. Is it only 7th-8th grade. Geez, I have to many unanswered questions.

@Finn Hulse
–
Science bowl is the best, I first got started in our schools science bowl club, it is really fun and you learn a lof different subects of science ask your teachers about it.

@Sharky Kesa
–
I feel sorry for you, but do you have any math competitions, You are 13 years old and you are level 5 in algebra, combinactoris and number theory.Nice!

@Finn Hulse
–
gosh y'all are so lucky; in Taiwan, we have like 2 hours of homework everyday (as in, at home).... -.- not to mention tests every three or so days.... uggg

good! Great going :) hope you guys become renowned for doing something better and new. All the best for Life and its challenges!
School is way awesome and Youth is gr8. But when it goes, you know where you stand and I hope, then you know where you want to go next.

I've always liked math a lot, but when I got to sixth grade, I realized it was cool to be really good at math. So I started becoming "fake"-good, at math just to be cool.

I realized that in fact, math was AWESOME in the summer after sixth grade. Now, I'm in 7th grade, and I do math because of how interesting and amazing it is.

Hi @Finn Hulse , it seems like you are very eager to be on the "People to Follow", hope you won't want to bite my head off for taking the place, haha. What I want to say is, "People to Follow" isn't a place to get attention, nor judging your achievements/ability. You are doing great and the "People to Follow" doesn't matter very much actually! Keep up your great job, cheers!

Haha, yes I am very eager to get on that list! I think your head should be pretty safe, though. It's just a matter of pride, for me. You know, like I just want to be considered a person to follow! Don't we all? :D

Thanks, you made my day! Actually, I'll be 13 in May. But yeah, I'm totally cool solving problems for fun, but on tests, I freak out and get a lot wrong. :D

@Finn Hulse
–
Just a salute? I admire you Finn Hulse dude you are awesome. I mean I am 15 and still I can't solve many problems but you , what can I say, FAB. I think this proficiency comes from AoPS. Am I right?

Oh yeah thanks. As a matter of fact, when I first joined Brilliant (with all Level 2's and 3's and 1's) I was originally Calculus Level 5. There was a really easy problem on the placement test. I accidentally lost it for a while, but then one of my wrong answers to @Sharky Kesa's Level 4 problem turned out to be right after all and my rating got pushed up! :D

Hugh Everett hypothesized that objective reality is actually many worlds, every event being a branch point spawning ever more possible worlds, so that in one world, the cat is alive, and in another, it's dead. Would you be a confirmation of that hypothesis, being that you seem to be everywhere and doing everything all at once?

@Michael Mendrin
–
Haha thanks. Yes I think roughly $\dfrac{1}{100000}$ of the currently existing universes contain a Finn Hulse who just had a Bar Mitzvah.

@Calvin Lin Could you boost the rating of Dominoes and Chessboards to like, 2200? It's pretty insanely tough until you realize the trick and then it's (moderately) easy. Good luck solving it! :D

Congratulations @Christopher Boo for beating me in terms of followers! I knew you would eventually, especially since you made "Who to Follow" and I didn't. Well, well, I guess I'll never be as good as you.

@Peter Taylor I'm happy to see that new bar where you can access solutions! I'm glad I don't need to upgrade to Brilliant Squared to have access to this decent little feature!

@Peter Taylor With the new solution-viewing format (where you can see what solutions you've posted) I had a "Brilliant" thought. What if when you viewed the page, beside each solution, it showed how many upvotes it had? Also, will you guys make it so we can view everybody's solutions, not just our own?

Recall that your problem had a wrong answer, and hence had an inflated rating. When we corrected it, the ratings were then pushed down. Given that it simply uses Newton formula, it's definitely not in level 5.

There is a possibility that the numbers are not accurate, given that we had to change the answer.

I see. But the numbers were unchanged, so I don't think that that would have done anything. Especially considering that the moment you changed the answer, the # of solvers went from 1 to 16. But Newton's Sums is still a Level 4 concept, especially in that application of it. I'd appreciate it if you gave it the correct rating. Thanks. :D

@Yan Yau Cheng I have a much simpler proof for problem #5.

Question Statement:

Given that $p$ and $p^2 + 8$ are both primes , what is the sum of all possible
values of $p$?

Solution:

We can see that if $p \equiv 1$ or $p \equiv 2 \pmod{3}$, then $p^2$ will be congruent to $1$ or $4$ modulo $3$, respectively (which is simply $1^2$ and $2^2$). In both of these cases, by adding $8$ which is $\equiv -1 \pmod{3}$, the expression is $\equiv 0 \pmod{3}$ and is thus never prime (it's divisible by $3$). For $p \equiv 0 \pmod{3}$, the expression is congruent to $0+8 \equiv 2 \pmod{3}$ which may or may not be prime. But because $3$ is the only prime divisible by $3$, we can just plug that in, which is $3^2+8=17$ which is prime. Thus $\boxed{3}$ is the only solution.

Yes! I attribute my recent change mostly to Brilliant Squared, though. Aside from that, @Anish Puthuraya's YouTube channel has been a great resource, along with Khan Academy and a Physics II for Dummies textbook. When I'm unfamiliar with an approach, Google is very helpful, and once I master a formula, I can apply it!

Oh yeah but also the thing about Brilliant Squared is that the problems are ranked way higher than they should be. I think it's mostly because the staff can choose the rating, even though in reality it gets pushed down a ton.

Oh. My name is Yuxuan (Yû Xuān) and Seah is my family name. In pinyin it's Shé.
I don't really know how to tell you how to pronounce it in English, because when people first see it, they usually get it wrong and I just adopt a Trial and Error method to help them get it right. But I could try :D

'See-ahh.' That's somewhat right.
(My Chinese name, in case you wanna know, is 佘宇轩.) :D
Try to teach yourself mandarin. It's fun. And educational. :D

@Yuxuan Seah
–
Sorry about the formatting though, for the 'û' the sign on top is actually inverted. (Couldn't get it right on my computer. D:) And yes, 'Seah' isn't in pinyin. o.O
Interesting that you ask such a question. :D

I didn't know your mom speaks Mandarin! Hmm... is she from China? Or Singapore? :D

That sounds really neat and fun, did your school has some kind of program that teaches you in math too?
And how many times did you practice in a week? Sorry for asking too many questions, I'm just too curious ><

@Calvin Lin Have you seen this epic problem!? I think it's really cool and takes advantage of one of the coolest algebraic principles that I know! You'll enjoy it! :D

1) $g(x)$ is a polynomial, otherwise I can define $|g(3) |$ to be anything.
2) The degree of $g(x)$ matters, otherwise we can take the square.
3) The leading coefficient of $g(x)$ matters, otherwise we can just multiply by 2.

@Finn Hulse
–
The polynomial $g(x) = (5(3)^5+3(3)^4-11(3)^3-2(3)^2+3(3)+5) ^2$ will also satisfy your conditions as previously stated, namely that each of the roots of $g(x)$ is the reciprocal of one of $f(x)$ roots.

Note that currently, saying "the coefficient of $x^5$ is -5 is also not sufficient, since I could take $g(x) = A(5(3)^5+3(3)^4-11(3)^3-2(3)^2+3(3)+5) ^2$ for some suitable constant $A$.

Note that you will also need the condition that "each of $f(x)$ roots are the reciprocal of $g(x)$ roots", otherwise, I can just take $\alpha x - 1$, where $f( \alpha ) = 0$.

The issue with some of your problems is that they are not correctly and clearly phrased. You have an idea of what it is in your head, but when written down, it could be interpreted in a multitude of ways. You need to take care of such 'edge cases' that I listed out above, instead of expecting others to deduce what you are thinking. They will not do so, and would instead just skip your problem.

@Calvin Lin
–
It's all Greek to me. Would you mind making the changes? I'm sorry for the inconveniences with all of these problems. I'll make sure to not make such silly mistakes in the future. :D

@Finn Hulse
–
I've made some changes which makes $g(x)$ uniquely determined (up to sign). There are possibly better ways of expressing it that are not so clunky.

I avoided talking about the "content of the polynomial", as that is not a commonly understood term.

Finn, can you please tell me what is the line between 10 and Euler's totient function in your problem "Let's compute this manually " in your " Modular arithmetic and NT problems " set ?

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

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## Comments

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TopNewestDoes your school have a strange schedule/lots of free periods? You seem to be able to get to a computer at all times of the day, I've been curious how you manage that with school/homework.

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HAHAHAHAHAHAHA! Yes, I have no life, and yes, except today, I spend roughly 2 hours on Brilliant. Which is tough because I'm preparing for a Bar-Mitzvah and I'm swimming. So yeah. I am a Brilliantic for life.

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Nice, it's pretty funny how you said you had no life, my friends tell me that all the time and make fun of me for getting on this website a lot. There all like, " oh ya Robert, your website is only for brilliant people. In a stupid sarcastic tone. Didn't know you were Jewish, that's pretty cool! What's your plan for your Bar-Mitzvah. My friend went to a nice hotel in Mexico and ate a ton of food. He said it was pretty freaking amazing.

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**!" Luckily, I heard my other school actually has a decent team. I guess I'll try it next year. Is it only 7th-8th grade. Geez, I have to many unanswered questions.Log in to reply

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That's what I've been thinking as well... then I remembered how blissfully delightful middle school was. Not much homework there.

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HAHAHAHAHA yeah. I haven't done any homework AT HOME since 4th grade. No joke. :D

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What do you like to do except "Brilling".!

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Math... and friends. Haha, I hadn't thought of Brilling. :D

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What is there to do in Willamsburg?

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Quite a lot! I just don't do any of it. Have you ever heard of Colonial Williamsburg? It was the capital for twice as long as Washington, D. C..

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are you really 13 years old? :D

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Uhh. Well im not ;) (5th grade)

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good! Great going :) hope you guys become renowned for doing something better and new. All the best for Life and its challenges! School is way awesome and Youth is gr8. But when it goes, you know where you stand and I hope, then you know where you want to go next.

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HAHAHAHAHAHAHAH nice. Fist bump for us young people. :D

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Finn Hulse .....hv guts attempt this

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@Finn hulse How/when you noticed you're smart in (math/physics &others...) at the first time ? How did u feel then? :)

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I've always liked math a lot, but when I got to sixth grade, I realized it was cool to be really good at math. So I started becoming "fake"-good, at math just to be cool.

I realized that in fact, math was AWESOME in the summer after sixth grade. Now, I'm in 7th grade, and I do math because of how interesting and amazing it is.

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Hi @Finn Hulse , it seems like you are very eager to be on the "People to Follow", hope you won't want to bite my head off for taking the place, haha. What I want to say is, "People to Follow" isn't a place to get attention, nor judging your achievements/ability. You are doing great and the "People to Follow" doesn't matter very much actually! Keep up your great job, cheers!

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Haha, yes I am very eager to get on that list! I think your head should be pretty safe, though. It's just a matter of pride, for me. You know, like I just want to be considered a person to follow! Don't we all? :D

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You should get an AoPS account.

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I have one, it's FINNN.

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Hey, I am not god! :P

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Dude. I will treat you as such.

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man! finn hulse! u r juss 13 yrs old nd u solve so many problems of higher levels with ease...! gr8! :)

saluteLog in to reply

Thanks, you made my day! Actually, I'll be 13 in May. But yeah, I'm totally cool solving problems for fun, but on tests, I freak out and get a lot wrong. :D

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oh ! den u r 12.... den a

bigger salute...Log in to reply

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Happy (belated) birthday Finn!!! Finally 13 :D I'm turning 13 in twelve more days (May 18)...

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Aww thanks dude! :D

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:) no prob

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Happy (probably belated) birthday, Finn!!!!! You're 13 and a teenager!!! I have 7 more months to wait.

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Lol, I'm almost there (twelve more days!~)

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@Finn Hulse Congrats on your level 4 and level 5 on all subjects especially calculus.

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Oh yeah thanks. As a matter of fact, when I first joined Brilliant (with all Level 2's and 3's and 1's) I was originally Calculus Level 5. There was a really easy problem on the placement test. I accidentally lost it for a while, but then one of my wrong answers to @Sharky Kesa's Level 4 problem turned out to be right after all and my rating got pushed up! :D

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Which question was this?

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$\zeta(0.5)$ where you had like the sign switched or something.

It was asking forLog in to reply

Hugh Everett hypothesized that objective reality is actually many worlds, every event being a branch point spawning ever more possible worlds, so that in one world, the cat is alive, and in another, it's dead. Would you be a confirmation of that hypothesis, being that you seem to be everywhere and doing everything all at once?

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That is interesting to think about. And yes, I am doing a lot at once. Yesterday I had my Bar Mitzvah... :O

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Mazel Tov!, to at least one of you anyway.

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$\dfrac{1}{100000}$ of the currently existing universes contain a Finn Hulse who just had a Bar Mitzvah.

Haha thanks. Yes I think roughlyLog in to reply

Hi Finn have you noticed that it is showing that you have followed only 51 members. Actually you had followed around 3000+ I suppose?

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Yeah. I thought it was a bug but it wasn't. Did you spend all your time unfollowing people?

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No I didn't . Why would I do that?

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No! It is a bug! :O

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@Sharky Kesa @Trevor B. That was the most freaking boss game of FTW! ever! We have to do that more. :D

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Definitely.

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What's FTW?

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YO FINN!!! For The Win. :D

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@Daniel Liu @William Cui @Franklyn Wang @Akshaj Kadaveru @Nicky Sun You guys! Good luck at Nationals! I can't wait to watch the CD round on ESPN! It's going to be so intense! Watch out for Colin Tang! :D

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@Dan Lawson Would you mind writing a solution to Plugging Roots into Functions? I'm really interested to see your technique. :D

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@Yan Yau Cheng When will JOMO 4 results be released? I really want to know how @Emery Shelly and I did! :D

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@Jon Haussmann @Daniel Liu @Pi Han Goh @Ashtik Mahapatra @Calvin Lin @Dinesh Chavan @Gabriel Merces @David Lee @Xuming Liang @Akshaj Kadaveru @Christopher Boo @Sharky Kesa And all others, try to solve and post a proof/solution to Two Maximized Constants in an Inequality. Good luck! :D

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@Calvin Lin Could you boost the rating of Dominoes and Chessboards to like, 2200? It's pretty insanely tough until you realize the trick and then it's (moderately) easy. Good luck solving it! :D

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Is that so? I don't really think it is that hard at all... I will post a solution.

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Oh awesome! :D

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Congratulations @Christopher Boo for beating me in terms of followers! I knew you would eventually, especially since you made "Who to Follow" and I didn't. Well, well, I guess I'll never be as good as you.

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@Peter Taylor I'm happy to see that new bar where you can access solutions! I'm glad I don't need to upgrade to Brilliant Squared to have access to this decent little feature!

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@Peter Taylor With the new solution-viewing format (where you can see what solutions you've posted) I had a "Brilliant" thought. What if when you viewed the page, beside each solution, it showed how many upvotes it had? Also, will you guys make it so we can view everybody's solutions, not just our own?

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@Finn Hulse I found someone who follows more people than you: @Santanu Banerjee

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Yeah, I had noticed that but assumed Finn knew.

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Yeah I did @Daniel Liu but can you find anybody with more comments than me? I'm like the most social person on the site. :D

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@Finn Hulse

If it was possible they would have millions of commentsLog in to reply

@Emil Svensson Do you actually live in Williamsburg VA?

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@Calvin Lin Have you actually received my email? Sorry to bug you, but I'm interested to see your reaction. :O

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@Calvin Lin How is the rating for Plugging Roots into Functions Level 3? Only 16/32 people have solved it which should make it Level 4-5. :/

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Recall that your problem had a wrong answer, and hence had an inflated rating. When we corrected it, the ratings were then pushed down. Given that it simply uses Newton formula, it's definitely not in level 5.

There is a possibility that the numbers are not accurate, given that we had to change the answer.

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I see. But the numbers were unchanged, so I don't think that that would have done anything. Especially considering that the moment you changed the answer, the # of solvers went from 1 to 16. But Newton's Sums is still a Level 4 concept, especially in that application of it. I'd appreciate it if you gave it the correct rating. Thanks. :D

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@Yan Yau Cheng I have a much simpler proof for problem #5.

Question Statement:

Given that $p$ and $p^2 + 8$ are both primes , what is the sum of all possible values of $p$?

Solution:

We can see that if $p \equiv 1$ or $p \equiv 2 \pmod{3}$, then $p^2$ will be congruent to $1$ or $4$ modulo $3$, respectively (which is simply $1^2$ and $2^2$). In both of these cases, by adding $8$ which is $\equiv -1 \pmod{3}$, the expression is $\equiv 0 \pmod{3}$ and is thus never prime (it's divisible by $3$). For $p \equiv 0 \pmod{3}$, the expression is congruent to $0+8 \equiv 2 \pmod{3}$ which may or may not be prime. But because $3$ is the only prime divisible by $3$, we can just plug that in, which is $3^2+8=17$ which is prime. Thus $\boxed{3}$ is the only solution.

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Whew, I'm not very active recently and I just found that you are all most level 5 in every topic! Do you have a great source to learn your physics?

By the way, I like your tag #Finn, added to my list! :P

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Yes! I attribute my recent change mostly to Brilliant Squared, though. Aside from that, @Anish Puthuraya's YouTube channel has been a great resource, along with Khan Academy and a Physics II for Dummies textbook. When I'm unfamiliar with an approach, Google is very helpful, and once I master a formula, I can apply it!

Oh yeah but also the thing about Brilliant Squared is that the problems are ranked way higher than they should be. I think it's mostly because the staff can choose the rating, even though in reality it gets pushed down a ton.

Oh yeah and #Finn is a pretty epic tag. :D

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Thanks! :D

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I added that tag the moment I realized you could add any tag to your homepage. :D

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My mom speaks Mandarin and I was wondering how you pronounce your last name, since I don't think it's in pinyin.

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@Yuxuan Seah.

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Oh. My name is Yuxuan (Yû Xuān) and Seah is my family name. In pinyin it's Shé. I don't really know how to tell you how to pronounce it in English, because when people first see it, they usually get it wrong and I just adopt a Trial and Error method to help them get it right. But I could try :D

'See-ahh.' That's somewhat right. (My Chinese name, in case you wanna know, is 佘宇轩.) :D Try to teach yourself mandarin. It's fun. And educational. :D

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I didn't know your mom speaks Mandarin! Hmm... is she from China? Or Singapore? :D

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Aww Finn, did'cha unfollow me? D: and what happened to Theme based problems. And hows the country ur in XP

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He hasn't left the country, I think, but the state. I am in a different country, SINGAPORE! :D

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COME VISIT RI XD even tho im not sure if they allow strangers in

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Hi Finn, did you take any math lessons outside the school? (i.e KUMON)

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Yes, a senior from the local college that my parents teach at comes over once a week to tutor me in advanced graduate-level math.

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Dude, you came back! Where have you been?

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That sounds really neat and fun, did your school has some kind of program that teaches you in math too? And how many times did you practice in a week? Sorry for asking too many questions, I'm just too curious ><

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Hi

Will you post a question anytime soon ?

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Sure!

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@Mardokay Mosazghi Dude, I loved this problem Super Finn to the Rescue. And yes, I love trampoline tricks. :D

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@Finn Hulse Thanks

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@Calvin Lin Have you seen this epic problem!? I think it's really cool and takes advantage of one of the coolest algebraic principles that I know! You'll enjoy it! :D

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Several edits are needed.

1) $g(x)$ is a polynomial, otherwise I can define $|g(3) |$ to be anything.

2) The degree of $g(x)$ matters, otherwise we can take the square.

3) The leading coefficient of $g(x)$ matters, otherwise we can just multiply by 2.

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Okay. Wow. Dang, you're good. :O

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What do you mean the degree of $g(x)$ matters?

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$g(x) = (5(3)^5+3(3)^4-11(3)^3-2(3)^2+3(3)+5) ^2$ will also satisfy your conditions as previously stated, namely that each of the roots of $g(x)$ is the reciprocal of one of $f(x)$ roots.

The polynomialNote that currently, saying "the coefficient of $x^5$ is -5 is also not sufficient, since I could take $g(x) = A(5(3)^5+3(3)^4-11(3)^3-2(3)^2+3(3)+5) ^2$ for some suitable constant $A$.

Note that you will also need the condition that "each of $f(x)$ roots are the reciprocal of $g(x)$ roots", otherwise, I can just take $\alpha x - 1$, where $f( \alpha ) = 0$.

The issue with some of your problems is that they are not correctly and clearly phrased. You have an idea of what it is in your head, but when written down, it could be interpreted in a multitude of ways. You need to take care of such 'edge cases' that I listed out above, instead of expecting others to deduce what you are thinking. They will not do so, and would instead just skip your problem.

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$g(x)$ uniquely determined (up to sign). There are possibly better ways of expressing it that are not so clunky.

I've made some changes which makesI avoided talking about the "content of the polynomial", as that is not a commonly understood term.

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Finn, can you please tell me what is the line between 10 and Euler's totient function in your problem "Let's compute this manually " in your " Modular arithmetic and NT problems " set ?

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$a|b$ means that $a$ is divisible by $b$.

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thank you ....

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No it means the opposite. So like $3 \mid 12$.

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