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Re: Sequence

This can be written as $\zeta(1)$ (don't be afraid if you never saw this, search for Zeta Function).
\[1+\dfrac12+\dfrac13+\ldots=\prod_{p\in\mathbb P}\dfrac{p}{p-1}\]
where $\mathbb P$ is the set of primes.
Why does this hold? Think using unique prime factorization.
by Masum
Sat Oct 10, 2015 12:26 am
 
Forum: Number Theory
Topic: Sequence
Replies: 3
Views: 596

Re: #Number Theory

See the article here.
viewtopic.php?f=26&t=3422
by Masum
Sat Oct 10, 2015 12:23 am
 
Forum: Number Theory
Topic: #Number Theory
Replies: 2
Views: 521

Thue's Lemma

Here is an article on Thue's Lemma.
by Masum
Sat Oct 10, 2015 12:22 am
 
Forum: Number Theory
Topic: Thue's Lemma
Replies: 0
Views: 418

Re: Good positive integers

Aha. That problem of mine! It's quite easy actually. But it can be made a bit hard with more restrictions. Have you solved it?
by Masum
Sat Oct 10, 2015 12:20 am
 
Forum: Number Theory
Topic: Good positive integers
Replies: 1
Views: 338

Re: Hi Everyone!

You are most welcome! :D
by Masum
Mon Sep 21, 2015 10:42 pm
 
Forum: Introductions
Topic: Hi Everyone!
Replies: 1
Views: 790

Re: ONTC Final Exam

now it should be correct
by Masum
Mon Sep 14, 2015 11:52 pm
 
Forum: National Math Camp
Topic: ONTC Final Exam
Replies: 34
Views: 3833

Re: ONTC Final Exam

tanmoy wrote:$2^{n}+1$ is odd.So,$n^{2}-1$ is odd.So,$n$ is even.Let $n=2k$.Then $2^{n}+1=(2^{k})^{2}+1$.So,every divisor of $2^{n}+1$ is of the form $4m+1$.
So,$n^{2}-1 \equiv 1 (mod 4)$.
Or,$n^{2} \equiv 2 (mod 4)$,which is impossible.
So there is no solution. :)

You have to prove it.
by Masum
Mon Sep 14, 2015 3:26 pm
 
Forum: National Math Camp
Topic: ONTC Final Exam
Replies: 34
Views: 3833

Re: ONTC Final Exam

Try this: $n^2-1|2^n+1$
by Masum
Sun Sep 13, 2015 11:16 pm
 
Forum: National Math Camp
Topic: ONTC Final Exam
Replies: 34
Views: 3833

Re: ONTC Final Exam

Ya, this is the way to do it.
by Masum
Sat Sep 12, 2015 7:22 pm
 
Forum: National Math Camp
Topic: ONTC Final Exam
Replies: 34
Views: 3833

Re: ONTC Final Exam

I posted the solutions of the first one in my new blog. But my laziness is getting the better of me again. When that passes, I will start writing again there. Stay tuned lol
by Masum
Mon Sep 07, 2015 1:18 am
 
Forum: National Math Camp
Topic: ONTC Final Exam
Replies: 34
Views: 3833
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