Waste less time on Facebook — follow Brilliant.
×

Finn Hulse's Messageboard

Everybody else is doing it, I might as well. Enjoy! :D

Note by Finn Hulse
2 years, 11 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

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. Sam Solomon Staff · 2 years, 11 months ago

Log in to reply

@Sam Solomon 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. Finn Hulse · 2 years, 11 months ago

Log in to reply

@Finn Hulse 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 · 2 years, 11 months ago

Log in to reply

@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 · 2 years, 11 months ago

Log in to reply

@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. Robert Fritz · 2 years, 11 months ago

Log in to reply

@Robert Fritz No, I've never done Science Bowl. But you should totally do MATHCOUNTS! It's fricking boss! :D Finn Hulse · 2 years, 11 months ago

Log in to reply

@Finn Hulse National Science Bowl (NSB) is something you should really consider doing! It was really fun last year. Do it for the experience. Daniel Liu · 2 years, 11 months ago

Log in to reply

@Daniel Liu How do I get started? Finn Hulse · 2 years, 11 months ago

Log in to reply

@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. Mardokay Mosazghi · 2 years, 11 months ago

Log in to reply

@Mardokay Mosazghi Oh. My school doesn't have a Science Bowl club. Can I still participate? Finn Hulse · 2 years, 11 months ago

Log in to reply

@Finn Hulse Yeah I think so Mardokay Mosazghi · 2 years, 11 months ago

Log in to reply

@Mardokay Mosazghi They have nothing like that in Australia. It's saddening. Sharky Kesa · 2 years, 11 months ago

Log in to reply

@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! Mardokay Mosazghi · 2 years, 11 months ago

Log in to reply

@Mardokay Mosazghi I have a couple which I am going to attend and also I am 12. Sharky Kesa · 2 years, 11 months ago

Log in to reply

@Sam Solomon That's what I've been thinking as well... then I remembered how blissfully delightful middle school was. Not much homework there. Justin Wong · 2 years, 11 months ago

Log in to reply

@Justin Wong HAHAHAHAHA yeah. I haven't done any homework AT HOME since 4th grade. No joke. :D Finn Hulse · 2 years, 11 months ago

Log in to reply

@Finn Hulse Same here I complete my homework at school and then either log on to Brilliant or enjoy Ashtik Mahapatra · 2 years, 11 months ago

Log in to reply

@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 Dana Chiueh · 2 years, 10 months ago

Log in to reply

@Dana Chiueh Me too Mardokay Mosazghi · 2 years, 10 months ago

Log in to reply

@Mardokay Mosazghi Dude you're in the US. :P Finn Hulse · 2 years, 10 months ago

Log in to reply

@Finn Hulse What if it's a special sort of school such as a selective school for highly academic or a grammar school. Sharky Kesa · 2 years, 10 months ago

Log in to reply

@Sharky Kesa He goes to Takoma Park. :P Finn Hulse · 2 years, 10 months ago

Log in to reply

@Finn Hulse no i got MBHS Mardokay Mosazghi · 2 years, 9 months ago

Log in to reply

@Mardokay Mosazghi Oh. But you used to go to Takoma right? Finn Hulse · 2 years, 9 months ago

Log in to reply

@Finn Hulse yep Mardokay Mosazghi · 2 years, 9 months ago

Log in to reply

@Dana Chiueh :O Finn Hulse · 2 years, 10 months ago

Log in to reply

@Finn Hulse i know it's so sad D: Dana Chiueh · 2 years, 10 months ago

Log in to reply

@Finn Hulse This is usually what happens in south and south-east Asia. I have done Kindergarten in India, I know (though not that much). Sharky Kesa · 2 years, 10 months ago

Log in to reply

@Sharky Kesa I went to the American Embassy School in Dehli. Needless to say, it was luxurious and easy. :D Finn Hulse · 2 years, 10 months ago

Log in to reply

@Finn Hulse ..........oh it's the "American Embassy" part eh? Dana Chiueh · 2 years, 10 months ago

Log in to reply

@Dana Chiueh Hmmm... Sharky Kesa · 2 years, 10 months ago

Log in to reply

@Sharky Kesa yup (although, technically, Taiwan is in east asia....) Dana Chiueh · 2 years, 10 months ago

Log in to reply

What do you like to do except "Brilling".! Satvik Golechha · 2 years, 11 months ago

Log in to reply

@Satvik Golechha Math... and friends. Haha, I hadn't thought of Brilling. :D Finn Hulse · 2 years, 11 months ago

Log in to reply

What is there to do in Willamsburg? Calvin Lin Staff · 2 years, 11 months ago

Log in to reply

@Calvin Lin 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.. Finn Hulse · 2 years, 11 months ago

Log 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? Michael Mendrin · 2 years, 9 months ago

Log in to reply

@Michael Mendrin That is interesting to think about. And yes, I am doing a lot at once. Yesterday I had my Bar Mitzvah... :O Finn Hulse · 2 years, 9 months ago

Log in to reply

@Finn Hulse Mazel Tov!, to at least one of you anyway. Michael Mendrin · 2 years, 9 months ago

Log in to reply

@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. Finn Hulse · 2 years, 9 months ago

Log in to reply

@Finn Hulse Congrats on your level 4 and level 5 on all subjects especially calculus. Mardokay Mosazghi · 2 years, 9 months ago

Log in to reply

@Mardokay Mosazghi 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 Finn Hulse · 2 years, 9 months ago

Log in to reply

@Finn Hulse Which question was this? Sharky Kesa · 2 years, 9 months ago

Log in to reply

@Sharky Kesa It was asking for \(\zeta(0.5)\) where you had like the sign switched or something. Finn Hulse · 2 years, 9 months ago

Log in to reply

Happy (probably belated) birthday, Finn!!!!! You're 13 and a teenager!!! I have 7 more months to wait. Sharky Kesa · 2 years, 10 months ago

Log in to reply

@Sharky Kesa Lol, I'm almost there (twelve more days!~) Dana Chiueh · 2 years, 10 months ago

Log in to reply

Happy (belated) birthday Finn!!! Finally 13 :D I'm turning 13 in twelve more days (May 18)... Dana Chiueh · 2 years, 10 months ago

Log in to reply

@Dana Chiueh Aww thanks dude! :D Finn Hulse · 2 years, 10 months ago

Log in to reply

@Finn Hulse :) no prob Dana Chiueh · 2 years, 10 months ago

Log in to reply

man! finn hulse! u r juss 13 yrs old nd u solve so many problems of higher levels with ease...! gr8! :) salute Pradeep Ch · 2 years, 11 months ago

Log in to reply

@Pradeep Ch 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 · 2 years, 11 months ago

Log in to reply

@Finn Hulse oh ! den u r 12.... den a bigger salute... Pradeep Ch · 2 years, 11 months ago

Log in to reply

@Pradeep Ch Haha, okay. :D Finn Hulse · 2 years, 11 months ago

Log in to reply

@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? Ashtik Mahapatra · 2 years, 11 months ago

Log in to reply

@Ashtik Mahapatra Oh actually no, I've never really used AoPS. I can't figure out how to get anywhere. :D Finn Hulse · 2 years, 10 months ago

Log in to reply

@Finn Hulse I also have an AoPS acc but I am confused its so messed up Ashtik Mahapatra · 2 years, 10 months ago

Log in to reply

@Ashtik Mahapatra Hahaha, if you say so. Finn Hulse · 2 years, 11 months ago

Log in to reply

Hey, I am not god! :P David Lee · 2 years, 11 months ago

Log in to reply

@David Lee Dude. I will treat you as such. Finn Hulse · 2 years, 11 months ago

Log in to reply

You should get an AoPS account. David Lee · 2 years, 11 months ago

Log in to reply

@David Lee I have one, it's FINNN. Finn Hulse · 2 years, 11 months ago

Log in to reply

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! Christopher Boo · 2 years, 11 months ago

Log in to reply

@Christopher Boo 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 Finn Hulse · 2 years, 11 months ago

Log in to reply

@Finn hulse How/when you noticed you're smart in (math/physics &others...) at the first time ? How did u feel then? :) Mahdi Al-kawaz · 2 years, 11 months ago

Log in to reply

@Mahdi Al-kawaz 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. Finn Hulse · 2 years, 11 months ago

Log in to reply

Finn Hulse .....hv guts attempt this Mayyank Garg · 2 years, 11 months ago

Log in to reply

are you really 13 years old? :D Nisarg Thakkar · 2 years, 11 months ago

Log in to reply

@Nisarg Thakkar Uhh. Well im not ;) (5th grade) David Lee · 2 years, 11 months ago

Log in to reply

@David Lee 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. Nisarg Thakkar · 2 years, 11 months ago

Log in to reply

@David Lee HAHAHAHAHAHAHAH nice. Fist bump for us young people. :D Finn Hulse · 2 years, 11 months ago

Log in to reply

@Finn Hulse :D Youth is beast. Sharky Kesa · 2 years, 11 months ago

Log in to reply

@Sharky Kesa :D Finn Hulse · 2 years, 11 months ago

Log in to reply

Hi

Will you post a question anytime soon ? Azhaghu Roopesh M · 2 years ago

Log in to reply

@Azhaghu Roopesh M Sure! Finn Hulse · 2 years ago

Log in to reply

Hi Finn, did you take any math lessons outside the school? (i.e KUMON) Ahmad Naufal Hakim Ashari · 2 years ago

Log in to reply

@Ahmad Naufal Hakim Ashari 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. Finn Hulse · 2 years ago

Log in to reply

@Finn Hulse 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 >< Ahmad Naufal Hakim Ashari · 2 years ago

Log in to reply

@Finn Hulse Dude, you came back! Where have you been? Sharky Kesa · 2 years ago

Log in to reply

Aww Finn, did'cha unfollow me? D: and what happened to Theme based problems. And hows the country ur in XP Charlton Teo · 2 years, 8 months ago

Log in to reply

@Charlton Teo He hasn't left the country, I think, but the state. I am in a different country, SINGAPORE! :D Sharky Kesa · 2 years, 8 months ago

Log in to reply

@Sharky Kesa COME VISIT RI XD even tho im not sure if they allow strangers in Charlton Teo · 2 years, 8 months ago

Log in to reply

@Charlton Teo I don't think I can. Go to the Science building in Jurong East tomorrow, you might see me in the afternoon. Sharky Kesa · 2 years, 8 months ago

Log in to reply

My mom speaks Mandarin and I was wondering how you pronounce your last name, since I don't think it's in pinyin. Finn Hulse · 2 years, 9 months ago

Log in to reply

@Finn Hulse @Yuxuan Seah. Finn Hulse · 2 years, 9 months ago

Log in to reply

@Finn Hulse 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 · 2 years, 9 months ago

Log in to reply

@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 Yuxuan Seah · 2 years, 9 months ago

Log in to reply

@Yuxuan Seah Well, names are complicated. Check this out: http://en.wikipedia.org/wiki/Wolfe+585,_Senior Yuxuan Seah · 2 years, 9 months ago

Log in to reply

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 Christopher Boo · 2 years, 9 months ago

Log in to reply

@Christopher Boo 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 Finn Hulse · 2 years, 9 months ago

Log in to reply

@Finn Hulse I added that tag the moment I realized you could add any tag to your homepage. :D Yuxuan Seah · 2 years, 9 months ago

Log in to reply

@Finn Hulse Thanks! :D Christopher Boo · 2 years, 9 months ago

Log in to reply

@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. Finn Hulse · 2 years, 9 months ago

Log in to reply

@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. :/ Finn Hulse · 2 years, 10 months ago

Log in to reply

@Finn Hulse 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. Calvin Lin Staff · 2 years, 10 months ago

Log in to reply

@Calvin Lin 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 Finn Hulse · 2 years, 10 months ago

Log in to reply

@Calvin Lin Have you actually received my email? Sorry to bug you, but I'm interested to see your reaction. :O Finn Hulse · 2 years, 10 months ago

Log in to reply

@Emil Svensson Do you actually live in Williamsburg VA? Finn Hulse · 2 years, 10 months ago

Log in to reply

@Finn Hulse I found someone who follows more people than you: @Santanu Banerjee Daniel Liu · 2 years, 10 months ago

Log in to reply

@Daniel Liu Yeah, I had noticed that but assumed Finn knew. Sharky Kesa · 2 years, 10 months ago

Log in to reply

@Sharky Kesa 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 Finn Hulse · 2 years, 10 months ago

Log in to reply

@Finn Hulse There should be a couple. Sharky Kesa · 2 years, 10 months ago

Log in to reply

@Sharky Kesa I don't think so dude! I haven't seen anybody with like more than 500! Finn Hulse · 2 years, 10 months ago

Log in to reply

@Finn Hulse How about some of the staff? You can't see how many comment they have made. Sharky Kesa · 2 years, 10 months ago

Log in to reply

@Sharky Kesa Yeah I know that is a problem. :O Finn Hulse · 2 years, 10 months ago

Log in to reply

@Finn Hulse If it was possible they would have millions of comments @Finn Hulse Mardokay Mosazghi · 2 years, 10 months ago

Log in to reply

@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? Finn Hulse · 2 years, 10 months ago

Log in to reply

@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! Finn Hulse · 2 years, 10 months ago

Log in to reply

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. Finn Hulse · 2 years, 10 months ago

Log in to reply

@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 Finn Hulse · 2 years, 10 months ago

Log in to reply

@Finn Hulse Is that so? I don't really think it is that hard at all... I will post a solution. Daniel Liu · 2 years, 10 months ago

Log in to reply

@Daniel Liu Oh awesome! :D Finn Hulse · 2 years, 10 months ago

Log in to reply

Log in to reply

@Yan Yau Cheng When will JOMO 4 results be released? I really want to know how @Emery Shelly and I did! :D Finn Hulse · 2 years, 10 months ago

Log in to reply

@Dan Lawson Would you mind writing a solution to Plugging Roots into Functions? I'm really interested to see your technique. :D Finn Hulse · 2 years, 10 months ago

Log in to reply

@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 Finn Hulse · 2 years, 10 months ago

Log in to reply

@Sharky Kesa @Trevor B. That was the most freaking boss game of FTW! ever! We have to do that more. :D Finn Hulse · 2 years, 11 months ago

Log in to reply

@Finn Hulse What's FTW? Finn C · 9 months, 1 week ago

Log in to reply

@Finn C YO FINN!!! For The Win. :D Finn Hulse · 9 months, 1 week ago

Log in to reply

@Finn Hulse Nice name BTW... (I'm talking about the Finn part... The Hulse part is... ok I guess) Finn C · 9 months, 1 week ago

Log in to reply

@Finn Hulse Haha... I guess its rhyme time. :D Finn C · 9 months, 1 week ago

Log in to reply

@Finn Hulse Definitely. Sharky Kesa · 2 years, 10 months ago

Log 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? Ashtik Mahapatra · 2 years, 11 months ago

Log in to reply

@Ashtik Mahapatra Yeah. I thought it was a bug but it wasn't. Did you spend all your time unfollowing people? Sharky Kesa · 2 years, 11 months ago

Log in to reply

@Sharky Kesa No I didn't . Why would I do that? Ashtik Mahapatra · 2 years, 11 months ago

Log in to reply

@Ashtik Mahapatra Was talking to Finn. Sorry Ashtik for the miscommunication. Sharky Kesa · 2 years, 11 months ago

Log in to reply

@Sharky Kesa No! It is a bug! :O Finn Hulse · 2 years, 11 months ago

Log in to reply

@Finn Hulse Yeah it is Ashtik Mahapatra · 2 years, 11 months ago

Log in to reply

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 ? Sriram Venkatesan · 2 years, 8 months ago

Log in to reply

@Sriram Venkatesan \(a|b\) means that \(a\) is divisible by \(b\). Sharky Kesa · 2 years, 8 months ago

Log in to reply

@Sharky Kesa No it means the opposite. So like \(3 \mid 12\). Finn Hulse · 2 years, 8 months ago

Log in to reply

@Finn Hulse LOL, fail! Could be used in the thing. Sharky Kesa · 2 years, 8 months ago

Log in to reply

@Sharky Kesa thank you .... Sriram Venkatesan · 2 years, 8 months ago

Log in to reply

@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 Finn Hulse · 2 years, 11 months ago

Log in to reply

@Finn Hulse 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. Calvin Lin Staff · 2 years, 11 months ago

Log in to reply

@Calvin Lin What do you mean the degree of \(g(x)\) matters? Finn Hulse · 2 years, 11 months ago

Log in to reply

@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 Staff · 2 years, 11 months ago

Log in to reply

@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 · 2 years, 11 months ago

Log in to reply

@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. Calvin Lin Staff · 2 years, 11 months ago

Log in to reply

@Calvin Lin Okay. Wow. Dang, you're good. :O Finn Hulse · 2 years, 11 months ago

Log in to reply

@Mardokay Mosazghi Dude, I loved this problem Super Finn to the Rescue. And yes, I love trampoline tricks. :D Finn Hulse · 2 years, 11 months ago

Log in to reply

@Finn Hulse @Finn Hulse Thanks Mardokay Mosazghi · 2 years, 11 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...