Life is strong but yet fragile. It's a paradox. It's both things, like quantum physics:It's a particle and a wave at the same time!

Note by A Former Brilliant Member
6 years, 1 month ago

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.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

The first and most sensible question:-

Do you like carrots?

- 6 years, 1 month ago

not really,tell me do you like carrots?

- 6 years, 1 month ago

Hey Mehul , do you have quadro phobia?

Hello Everyone!!!

- 6 years, 1 month ago

Hello!

- 6 years, 1 month ago

Hey

- 6 years, 1 month ago

Can you help me out with this?

- 6 years, 1 month ago

Do you like carrots?

- 6 years, 1 month ago

I too have great interest in quantum physics and relativity .Keep eating carrots like Nihar because you too have the same number of letters in your name as is in carrots.I hope that you might solve the conflict of gravity and quantum mechanics in future.

- 6 years, 1 month ago

so you want to do career in pure physics or something else?

- 6 years, 1 month ago

It is very difficult for me to answer this question because of my wide range of interest in subjects of Mathematics,Physics,Computer Science and Astronomy.

- 6 years, 1 month ago

which subject do you like other than mathematics and physics.

- 6 years, 1 month ago

Computer Science and Astronomy.

- 6 years, 1 month ago

Bonne journee is not literally used as 'good day' in francais. It's more like have a good day. Sorry to ruin it. :3

And potato or potato?

- 6 years, 1 month ago

Got it thanks for that bro .Actually i am learning German not french

- 6 years, 1 month ago

(http://shivamani patil)

- 5 years, 8 months ago

Sorry I was practicing to make the link . The blue one...

- 5 years, 8 months ago

I wanted to spam :P

- 5 years, 8 months ago

Please as you are a moderator do check this problem. Chinmay Sangawadekar

- 5 years, 8 months ago

Formatting is alright.

- 5 years, 8 months ago

Still it is not getting the rating.

- 5 years, 8 months ago

Be patient , it will get rated as more and more people view it. If you have a valid reason for urgency for rating it , please tell .

- 5 years, 8 months ago

@Chinmay Sangawadekar, i see that you have interest in contributing to wikis like multiplicative functions and mobius function. talk to me at slack so we could make the wiki better.

- 5 years, 7 months ago

Brother , I have no access to slack , when I try , it says you are already invited , but I had deleted my emails already :( is there another way to communicate ? On Facebook ? @Aareyan Manzoor

- 5 years, 7 months ago

- 5 years, 7 months ago

How is it ? @Aareyan Manzoor

- 5 years, 7 months ago

oh yes that is cool... back to the topic of sections now. lets decide that what section are required for the wiki?

- 5 years, 7 months ago

First intro. then theorem(definition) then proof(if necessary) (examples)

- 5 years, 7 months ago

i enter my email and pass and got Sorry, you entered an incorrect email address or password.

- 5 years, 7 months ago

Yeah same here , @Dev Sharma

- 5 years, 7 months ago

https://crypto.stanford.edu/pbc/notes/numbertheory/mult.html , do check this out , it has many useful things which we can use for wiki

- 5 years, 7 months ago

cool, just went through it.... i was planning to include those sums....

- 5 years, 7 months ago

Yeah those are really awesome , so i have a plan , I will provide you with the stuff ,you select it and then tell me , then we will add those on wiki

- 5 years, 7 months ago

ok.. that is a good plan... it is going to become overcrowded your message board. try facebook. i have the same username as brilliant (aareyan manzoor).

- 5 years, 7 months ago

Sure I will add you immediately

- 5 years, 7 months ago

- 5 years, 7 months ago

okay ,

- 5 years, 7 months ago

go here for the wiki. what level audience do we target?

- 5 years, 7 months ago

I think we should aim for high level audience

- 5 years, 7 months ago

same in my mind. how 'bout lvl 3-5?

- 5 years, 7 months ago

Sure , first we will make it for level 3-4 then we will ask Calvin Lin for guidance , then we go for advance

- 5 years, 7 months ago

ok. the sections of the wiki then... how are we going to divide it?

- 5 years, 7 months ago

now what sections are we going to divide the wiki in?

- 5 years, 7 months ago

Does this mean , that n^{2015}=1 , ?

- 5 years, 7 months ago

Yes, "primitive root of unity" means that 2015 is the smallest positive integer $k$ such that $\omega^k=1$.

- 5 years, 7 months ago

@Otto Bretscher , can you tell me a general formula to find the product of totient of divisors of any number n

- 5 years, 6 months ago

@Isaac Buckley why did you choose Computer Sci. topic for this problem of yours ?

- 5 years, 6 months ago

Can you solve it using number theory?

- 5 years, 6 months ago

I dont know but problem looks like NT problem. Can you solve it by NT any tries ?

- 5 years, 6 months ago

I'm not going to say you can't... but if anyone could... they would be a God in the eyes of mathematicians.

- 5 years, 6 months ago

Oh yeah there is no specific formats for primes iant it?@Isaac Buckley

- 5 years, 6 months ago

I'd love to see anyone try to solve it with number theory, a great prize awaits them.

- 5 years, 6 months ago

M primes are so hard to find using comp. sci, i dont think number theory is the right approach!

- 5 years, 6 months ago

Really , well is there any generelization for primes,in such form ? @Isaac Buckley

- 5 years, 6 months ago

this

- 5 years, 6 months ago

Well I'm not sure what you mean by that exactly. $2^n-1$ is a possible prime only if $n$ is prime. That's all I can say about this form.

Something you might be interesting in reading up on is Mills' constant. It's a way to find primes. It has major short comings though, still interesting.

- 5 years, 6 months ago

Yes, but mills constant is hard to use as we need to have a good degree of acuracy!

- 5 years, 6 months ago

Exactly! But it's still amazing that such a constant exists. It's also not known if it rational or not.

- 5 years, 6 months ago

It is suprising how many numbers are yet to be proven irrational. for example $e+\pi$ is not proven to be irrational.

- 5 years, 6 months ago

Yeah, I love problems like that. I might actually post a problem relating to $e+\pi$ later tonight. It came up in a past exam paper I took. If mills' constant was rational the implications could be pretty big, you could possibly (by magic) find its exact fraction and thus generate as many primes as you want.

- 5 years, 6 months ago

Cool, maybe then someone might use it to prove the riemenn hypothesis!

- 5 years, 6 months ago

Is it like that ?

- 5 years, 6 months ago

Oh yes I agree with Aareyan, and thanks for the link.btw dont forget to try my problems and sorry for self advertising .;)

- 5 years, 6 months ago

You there ?@Isaac Buckley

- 5 years, 6 months ago

Is $2^n - 1$ a sure prime or is it not sure for prime $n$? @Isaac Buckley

- 5 years, 6 months ago

Only 49 n's have been found such that $2^n-1$ iss prime..... so no!

- 5 years, 6 months ago

Oh thanks for that info ..

- 5 years, 6 months ago

It's just a prime candidate. Try and prove that if n is composite then $2^n-1$ is also composite.

- 5 years, 6 months ago

sure ,

- 5 years, 6 months ago

I didn't, I chose number theory which was then changed to computer science by a moderator. I do not contest to it, it fits well in computer science.

- 5 years, 6 months ago

@Aareyan Manzoor , @Nihar Mahajan , dont you think this is level 5 problem ?Somebody set level 3 for it.

- 5 years, 6 months ago

It is okay. it doesnt use any hard concepts.

- 5 years, 6 months ago

see thishttps://brilliant.org/problems/double-polynomials/?group=3Bg9df1xnfS9&ref_id=1094417 shouldnt it be lvl 5 ???

- 5 years, 6 months ago

I think it must be level 3 only. Also , you must mention what $\phi$ function is.

- 5 years, 6 months ago

Hey @Nihar Mahajan take a look at this I strongly feel that this problem should get level 5 (though it has no advanced concepts)atleast 200 or 195 points.Please do update the seed level.I will be very thankfull to you

- 5 years, 6 months ago

Done. I think this is harder then the previous ones.

- 5 years, 6 months ago

@Chinmay Sangawadekar in the future please dont tag mods like this, if a mod comes across a problem he will change the level. By tagging you are bothering them, mods are usually busy.

- 5 years, 6 months ago

@Aareyan Manzoor see the link of problem

- 5 years, 6 months ago

@Nihar Mahajan , have you started learning limits ?

- 5 years, 6 months ago

I have finished it.

- 5 years, 6 months ago

Great What source ? M Prakash notes ? @Nihar Mahajan

- 5 years, 6 months ago

Calculus will be done in MPA during June-July. But due to curiosity I am learning it on my own.

- 5 years, 6 months ago

Hmm , so no school today for you ? @Nihar Mahajan

- 5 years, 6 months ago

Nope, its saturday.

- 5 years, 6 months ago

Well ,also see my level two limits problem ,this@Nihar Mahajan

- 5 years, 6 months ago

Yes , sure.

- 5 years, 6 months ago

- 5 years, 6 months ago

grt :)

- 5 years, 6 months ago

Post more limit problems please, thanks :)

- 5 years, 6 months ago

Hey why dont you try and solve my NT and Algebra lvl 4-5 problems ?@Nihar Mahajan

- 5 years, 6 months ago

Why don't you solve my all previous problems? @Chinmay Sangawadekar

- 5 years, 6 months ago

I was doing them only I did many of your recent problems @Nihar Mahajan

- 5 years, 6 months ago

@Nihar Mahajan what is the teamdomain of brilliant on slack ?

- 5 years, 6 months ago

@Nihar Mahajan you may try this

- 5 years, 6 months ago

Thanks , I got it :)

- 5 years, 6 months ago

@Nihar Mahajan , can you update my solution number ? I have written 6 and deleted my previous one so , can you do that ? or tell any staff member to do so ?

- 5 years, 6 months ago

Sorry , I can't do that , you may ask Calvin on his messageboard.

- 5 years, 6 months ago

@Nihar Mahajan , you may also try this

- 5 years, 6 months ago

@Chinmay Sangawadekar You may try this , this .

- 5 years, 5 months ago

solved ,,sorry ,, saw your comment now ,, Nice problems ..

- 5 years, 5 months ago

@Nihar Mahajan try these problems ;) 1 , and 2

- 5 years, 5 months ago

@Abhishek Sinha , Sorry to mention you here , but I wanted to know more about the Mathematics Department of MIT Can I get in there ? What is the process to do so ? Please tell.. Also , what is your PhD topic ?

- 5 years, 5 months ago

You should apply. The application procedure is publicly available. I am working on Network Control and Information Theory. Good luck!

- 5 years, 5 months ago

@Otto Bretscher : Please see if it is true : We have , $a\equiv 1\mod b$ where , $(a,b)$ are consecutive natural numbers such that , $a> b$ , then , $a^{n}\equiv 1\mod bn$ , this congruence is true .

- 5 years, 5 months ago

No, this is not correct (unless I misunderstand your statement). As a counterexample, consider $n=2, b=3, a=4$.

- 5 years, 5 months ago

Yeah right,,,btw also try my recent problem More Modular in 2016

- 5 years, 5 months ago

hi

- 5 years, 5 months ago

@Otto Bretscher sorry to mention you here , but in this problem , I have added 1 to the lambda function , so deno. Won't be 0 ...

- 5 years, 5 months ago

Are we talking about the Liouville function as usual? That one takes the vales 1 and -1.

- 5 years, 5 months ago

There is no fun in doing Number Theory without you...:(

- 5 years, 5 months ago

I really don't want to post any more problems... then I have to deal with some of these obnoxious guys when they post solutions. Maybe I will give you some ideas and you can post, Comrade!

- 5 years, 5 months ago

I am really sorry , all this has happened because of me ...:( @Otto Bretscher

- 5 years, 5 months ago

- 5 years, 5 months ago

@Otto Bretscher can you link me to some solutions like this, sorry if your experience in brilliant is harmed by them.

- 5 years, 5 months ago

- 5 years, 5 months ago

I really don't want to post any more problems... then I have to deal with some of these obnoxious guys when they post solutions.

these solutions posted by obnoxious guys.

- 5 years, 5 months ago

I don't want to name names, but I think you know the type.

- 5 years, 5 months ago

yes, i think i will go through your profile searching on my own for these guys.

- 5 years, 5 months ago

Aareyan please take strict actions for people like him...

- 5 years, 5 months ago

Humble Request: Please don't stop posting problems because of obnoxious guys. You are a crucial part of community and so are your problems. We enjoy your problems very much. If some guys are troubling you by any means , you may report it in private or on message board of any staff and the staff will take the appropriate action. Grooming math enthusiasts and comrades like Chinmay , Aareyan , me need your help on Brilliant , but if you stop posting problems like this for some reason you are not responsible for , we would be discouraged :(

- 5 years, 5 months ago

i agree; without his problem i never would have learned abt half the things iknow now, please dont stop otto sir; you are one of the best problem posters here.

- 5 years, 5 months ago

I agree with you aareyan...and Nihar...

- 5 years, 5 months ago

Oh lord no! Your problems are really integral to the community, sir. Please don't stop posting problems. As Nihar rightly did point out, you may report any such action to the staff, so that appropriate action can be taken. But please don't stop posting problems! :(

- 5 years, 5 months ago

Please look into my latest problem , Gauss won't help,, it is getting a lot of reports , but still I think problem may be right...help me comrade...

- 5 years, 5 months ago

It's great problem and your answer is correct, Comrade. You should write the Legendre symbol more clearly as $\left(\frac{n(n+1)}{10009}\right)$ though

- 5 years, 5 months ago

@Otto Bretscher dsorry to disturb you ...https://brilliant.org/problems/more-problems-in-2016-part-11/?group=JgjXt4dJvxew&ref_id=113

- 5 years, 4 months ago

@Aareyan Manzoor @Sharky Kesa see this problem......

- 5 years, 4 months ago

404 is a palindrome in base: -31

- 5 years, 4 months ago

Check my profile then...

- 5 years, 4 months ago

this and this

Kindly see into those problems...They are getting low response and also they are waiting for your awesome solutions...;)

- 5 years, 4 months ago

Looks like everybody is busy at school or work, including myself ;)

- 5 years, 4 months ago