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ShBh
  • Member for 6 years, 11 months
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53 votes
0 answers
2k views

A Nice Problem In Additive Number Theory

21 votes
0 answers
4k views

In Search Of Elementary Proof Of Kobayashi's Theorem

18 votes
2 answers
2k views

Let $T$ be any subset of $\{1,2,3,...,100\}$ with $69$ elements. Prove that one can find four distinct integers such that $a+b+c=d$.

13 votes
2 answers
767 views

A Pigeonhole-Principle from IMO Shortlist.

12 votes
3 answers
672 views

Prove that $\prod_{1\leq i,j\leq n}\frac{1+a_ia_j}{1-a_ia_j}\geq1$ for $n$ real numbers $a_i\in(-1,1)$

7 votes
3 answers
272 views

Some Combinatorics and Some Prime Numbers

6 votes
1 answer
435 views

A Combination of Graph Theory and Number Theory

5 votes
0 answers
301 views

Reciprocal of a Liouville number is also a Liouville number

5 votes
1 answer
224 views

Applications of Tits' alternative in number theory

4 votes
2 answers
139 views

Let $G$ be a group with a free subgroup of rank $2$. Let $H\leq G$ be such that $[G:H]<\infty$. Then $H$ also contains a free subgroup of rank $2$.

4 votes
2 answers
163 views

a question on prime numbers and infinite series

4 votes
1 answer
593 views

Turning An Algebraic Number Into An Algebraic Integer

4 votes
0 answers
104 views

A Nice Combinatorial Problem

4 votes
2 answers
402 views

Commutative Semigroup

4 votes
1 answer
131 views

Let $f,g\in\mathscr{R}[a,b]$ and $f,g\geq0$ such that $\left\{\int_{a}^{b}f(x)^pdx\right\}^{\frac{1}{p}}=0$. Prove that $\int_{a}^{b}f(x)g(x)dx=0$

3 votes
0 answers
286 views

A Combinatorial Geometry Problem With A Solution Using Extremal Principle

3 votes
1 answer
345 views

Generalization of an IMO 1985 Problem in Elementary Number Theory and Combinatorics.

3 votes
0 answers
114 views

Is my proof of the identity $\sum_{n=0}^{\infty}\ln(1+x^{2^n})=-\ln(1-x)$ correct?

3 votes
1 answer
204 views

Proving Irreducibility of $X^{2p}+pX^n-1$ in $\mathbb{Z}[X]$

3 votes
1 answer
154 views

Is every non-commutative ring a subring of $\operatorname{End}(V)$ for some vector space $V$?

2 votes
0 answers
154 views

How To Solve The Congruence $n\equiv1\pmod{\tau(n)}$

2 votes
1 answer
212 views

The Hedgehog space obtained from $\mathbb{R}^2$ with the Hedgehog metric is non-separable.

2 votes
2 answers
121 views

Find all $f(X)\in\mathbb{Z}[X]$ such that $\left(\frac{f(n)}{p}\right)=\left(\frac{n}{p}\right)$ [Legendre symbol and $p$ is a fixed prime]

2 votes
0 answers
110 views

Number of ways to arrange numbers in matrix in A.P.

2 votes
3 answers
246 views

Proving $p_{n+1}<p_n^2$ without Bertrand's postulate

2 votes
1 answer
199 views

Subrings of a Noetherian ring which inherits the Noetherian property

1 vote
1 answer
157 views

Why $\dim H^0(\hat{\mathbb{Z}},V)=\dim H^1(\hat{\mathbb{Z}},V)$ when $V$ is a finite $\hat{\mathbb{Z}}$-module?

1 vote
1 answer
142 views

A Question From Pigeon Hole Principle and Three Dimensional Tiling [closed]

1 vote
1 answer
278 views

Random Walk Around A Circle

0 votes
0 answers
93 views

How to Prove That Branch Points Of $\log (f(z))$ are Zeros and Poles of $f(z)$?