User Shubhrajit Bhattacharya

42 votes

0 answers

1k views

A Nice Problem In Additive Number Theory

asked Jul 9, 2020 at 5:32

17 votes

2 answers

1k views

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

combinatorics pigeonhole-principle

asked Oct 15, 2017 at 8:00

14 votes

0 answers

2k views

In Search Of Elementary Proof Of Kobayashi's Theorem

number-theory elementary-number-theory prime-numbers diophantine-approximation geometry-of-numbers

asked Dec 16, 2019 at 9:28

13 votes

2 answers

658 views

A Pigeonhole-Principle from IMO Shortlist.

combinatorics elementary-number-theory contest-math pigeonhole-principle

asked Nov 6, 2017 at 8:25

7 votes

3 answers

224 views

Some Combinatorics and Some Prime Numbers

combinatorics number-theory polynomials prime-numbers alternative-proof

asked May 14, 2020 at 14:41

6 votes

1 answer

407 views

A Combination of Graph Theory and Number Theory

combinatorics elementary-number-theory discrete-mathematics graph-theory contest-math

asked Jan 16, 2018 at 7:09

5 votes

0 answers

151 views

Reciprocal of a Liouville number is also a Liouville number

number-theory solution-verification transcendental-numbers diophantine-approximation liouville-numbers

asked Sep 2, 2020 at 15:38

5 votes

1 answer

186 views

Applications of Tits' alternative in number theory

number-theory free-groups geometric-group-theory solvable-groups

asked Jul 13, 2020 at 9:41

4 votes

2 answers

92 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 $2$.

abstract-algebra group-theory free-groups geometric-group-theory combinatorial-group-theory

asked Jul 16, 2020 at 16:26

4 votes

2 answers

127 views

a question on prime numbers and infinite series

sequences-and-series elementary-number-theory prime-numbers irrational-numbers

asked Oct 12, 2017 at 17:47

4 votes

1 answer

179 views

Turning An Algebraic Number Into An Algebraic Integer

abstract-algebra number-theory algebraic-number-theory algebraic-numbers

asked Jun 15, 2020 at 18:26

4 votes

0 answers

99 views

A Nice Combinatorial Problem

combinatorics contest-math binomial-coefficients extremal-combinatorics

asked Dec 8, 2019 at 17:57

4 votes

2 answers

206 views

Commutative Semigroup

abstract-algebra group-theory proof-writing semigroups binary-operations

asked Oct 11, 2018 at 16:41

4 votes

1 answer

115 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 $\int_{a}^{b}f(x)g(x)dx=0$

real-analysis calculus integration solution-verification riemann-integration

asked Aug 25, 2020 at 20:25

3 votes

0 answers

247 views

A Combinatorial Geometry Problem With A Solution Using Extremal Principle

combinatorics contest-math combinatorial-geometry extremal-combinatorics combinatorial-proofs

asked Jan 18, 2018 at 18:15

3 votes

1 answer

272 views

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

combinatorics elementary-number-theory pigeonhole-principle additive-combinatorics

asked Sep 9, 2017 at 20:42

3 votes

0 answers

106 views

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

calculus power-series solution-verification

asked Jul 30, 2020 at 18:35

3 votes

1 answer

166 views

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

number-theory polynomials prime-numbers solution-verification irreducible-polynomials

asked Jul 6, 2020 at 19:12

3 votes

1 answer

104 views

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

ring-theory vector-spaces noncommutative-algebra ring-isomorphism

asked Nov 25, 2019 at 23:16

2 votes

0 answers

148 views

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

number-theory elementary-number-theory modular-arithmetic congruence-relations

asked May 14, 2020 at 12:56

2 votes

1 answer

159 views

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

real-analysis metric-spaces solution-verification separable-spaces

asked Sep 8, 2020 at 21:25

2 votes

2 answers

95 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]

number-theory elementary-number-theory polynomials modular-arithmetic quadratic-residues

asked Jan 2, 2021 at 15:30

2 votes

0 answers

97 views

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

combinatorics contest-math

asked Feb 14, 2018 at 16:17

2 votes

3 answers

206 views

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

number-theory elementary-number-theory discrete-mathematics inequality prime-numbers

asked Feb 19, 2018 at 17:07

2 votes

1 answer

125 views

Subrings of a Noetherian ring which inherits the Noetherian property

abstract-algebra ring-theory commutative-algebra solution-verification noetherian

asked Aug 28, 2020 at 16:43

1 vote

1 answer

66 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?

number-theory homology-cohomology homological-algebra group-cohomology galois-cohomology

asked Jun 15, 2021 at 8:03

1 vote

1 answer

129 views

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

combinatorics pigeonhole-principle tiling

asked Sep 10, 2017 at 7:55

1 vote

1 answer

199 views

Random Walk Around A Circle

probability markov-chains markov-process random-walk

asked Jul 25, 2020 at 8:54

0 votes

0 answers

29 views

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

complex-analysis complex-numbers branch-cuts branch-points

asked Feb 17, 2021 at 18:08

0 votes

1 answer

58 views

How Can I Prove This Convergent Series Problem?

calculus sequences-and-series logarithms

asked Oct 22, 2017 at 9:33

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38 Questions

A Nice Problem In Additive Number Theory

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

In Search Of Elementary Proof Of Kobayashi's Theorem

A Pigeonhole-Principle from IMO Shortlist.

Some Combinatorics and Some Prime Numbers

A Combination of Graph Theory and Number Theory

Reciprocal of a Liouville number is also a Liouville number

Applications of Tits' alternative in number theory

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 $2$.

a question on prime numbers and infinite series

Turning An Algebraic Number Into An Algebraic Integer

A Nice Combinatorial Problem

Commutative Semigroup

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 $\int_{a}^{b}f(x)g(x)dx=0$

A Combinatorial Geometry Problem With A Solution Using Extremal Principle

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

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

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

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

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

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

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]

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

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

Subrings of a Noetherian ring which inherits the Noetherian property

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

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

Random Walk Around A Circle

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

How Can I Prove This Convergent Series Problem?