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C.S.
  • Member for 8 years, 10 months
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19 votes
16 answers
2k views

How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$

15 votes
4 answers
1k views

How does one evaluate $\int \frac{\sin(x)}{\sin(5x)} \ dx$

13 votes
2 answers
277 views

If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.

7 votes
1 answer
181 views

Relatively prime elements forming an arithmetic progression

6 votes
3 answers
150 views

$\sum_{n=1}^{\infty}\frac{1}{n^2} <\frac{33}{20}$ using elementary inequalities

4 votes
4 answers
263 views

How to prove: $\sum_{k=m+1}^{n} (-1)^{k} \binom{n}{k}\binom{k-1}{m}= (-1)^{m+1}$

4 votes
1 answer
105 views

Does $[G:Z(G)] =n \implies x \mapsto x^{n}$ a group homomorphism?

4 votes
2 answers
919 views

$G$ finite group with $H \leq G$ with $G = \bigcup_{g \in G} gHg^{-1} \implies H=G$

4 votes
1 answer
165 views

Find all $(x,y) \in \mathbb{N} \times \mathbb{N}$ such that $5^{x}+3^{y}$ is a perfect square

3 votes
1 answer
487 views

Finding all triplets of positive integers with certain property

3 votes
3 answers
156 views

If $d=\gcd\,(f(0),f(1),f(2),\cdots,f(n))$ then $d|f(x)$ for all $x \in \mathbb{Z}$

3 votes
1 answer
106 views

If $f,g$ are $2$ onto homomorphisms, $\exists$ $y \neq e \in M$ such that $f(y)=g(y)$.

2 votes
1 answer
56 views

Showing that $c_{i}\equiv 0\pmod{p}$

2 votes
1 answer
66 views

Counting the number of inversions for the function $f(x+yp)=qx+y$

2 votes
2 answers
123 views

Number of solutions to $a^2-b^2+c^2 = k\pmod{p}$

0 votes
2 answers
109 views

Showing $\int_{0}^{1}\frac{\log(1+x+x^{2}+\cdots+x^{2^{k}-1})}{x}\,dx <2-\frac{1}{2^{k-1}}$ [closed]

0 votes
1 answer
42 views

Only one prime factor of $2^{2^{k}}-1$ of the form $3\pmod{4}$