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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

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!

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! :(

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 :(

@Nihar Mahajan
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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.

@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 .

@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 ?

@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 ?

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

@A Former Brilliant Member
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@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.

@A Former Brilliant Member
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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.

@Aareyan Manzoor
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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.

@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.

@Aareyan Manzoor
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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

@A Former Brilliant Member
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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).

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

@A Former Brilliant Member
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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 .

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.

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.

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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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## Comments

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TopNewest@Otto Bretscher

this and this

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

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

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

this

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404 is a palindrome in base: -31

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Check my profile then...

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

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@Otto Bretscher

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...

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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

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@Otto Bretscher

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

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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!

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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! :(

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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 :(

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

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these solutions posted by obnoxious guys.

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

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@Chinmay Sangawadekar

Not at all... you are my best Comrade here,Log in to reply

@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 ...

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

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hi

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@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 .

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

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

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@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 ?

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

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

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@Chinmay Sangawadekar You may try this , this .

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

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@Nihar Mahajan , you may also try this

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@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 ?

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

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@Nihar Mahajan you may try this

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Thanks , I got it :)

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

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@Nihar Mahajan , have you started learning limits ?

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I have finished it.

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Great What source ? M Prakash notes ? @Nihar Mahajan

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@Nihar Mahajan

Hey why dont you try and solve my NT and Algebra lvl 4-5 problems ?Log in to reply

@Chinmay Sangawadekar

Why don't you solve my all previous problems?Log in to reply

@Nihar Mahajan

I was doing them only I did many of your recent problemsLog in to reply

@Nihar Mahajan

Hmm , so no school today for you ?Log in to reply

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this@Nihar Mahajan

Well ,also see my level two limits problem ,Log in to reply

@Chinmay Sangawadekar

Solved it.Log in to reply

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@Aareyan Manzoor see the link of problem

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

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

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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

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@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.

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It is okay. it doesnt use any hard concepts.

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

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

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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.

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Can you solve it using number theory?

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

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@Isaac Buckley

Really , well is there any generelization for primes,in such form ?Log in to reply

$2^n-1$ is a possible prime only if $n$ is prime. That's all I can say about this form.

Well I'm not sure what you mean by that exactly.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.

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

IsLog in to reply

$2^n-1$ is also composite.

It's just a prime candidate. Try and prove that if n is composite thenLog in to reply

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$2^n-1$ iss prime..... so no!

Only 49 n's have been found such thatLog in to reply

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@Isaac Buckley

You there ?Log in to reply

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$e+\pi$ is not proven to be irrational.

It is suprising how many numbers are yet to be proven irrational. for exampleLog in to reply

$e+\pi$ 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.

Yeah, I love problems like that. I might actually post a problem relating toLog in to reply

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this

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

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@Isaac Buckley

Oh yeah there is no specific formats for primes iant it?Log in to reply

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

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@Otto Bretscher , I wanted ask you about this

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

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

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@Chinmay Sangawadekar, lets talk about multiplicative function wiki first.

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okay ,

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

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@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.

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

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

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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

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login here. i had the same problems....

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@Dev Sharma

Yeah same here ,Log in to reply

@Aareyan Manzoor

How is it ?Log in to reply

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

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I wanted to spam :P

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Still it is not getting the rating.

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

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Chinmay Sangawadekar

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(http://shivamani patil)

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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?

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

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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.

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which subject do you like other than mathematics and physics.

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Computer Science and Astronomy.

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

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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.

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Do you like carrots?

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The first and most sensible question:-

Do you like carrots?

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Hey Mehul , do you have quadro phobia?

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not really,tell me do you like carrots?

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Hello Everyone!!!

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Can you help me out with this?

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Hello!

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Hey

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