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Top Questions
53
votes
A Nice Problem In Additive Number Theory
number-theory
inequality
trigonometric-series
exponential-sum
additive-combinatorics
asked Jul 9, 2020 at 5:32
math.stackexchange.com
21
votes
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
math.stackexchange.com
18
votes
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
math.stackexchange.com
13
votes
A Pigeonhole-Principle from IMO Shortlist.
combinatorics
elementary-number-theory
contest-math
pigeonhole-principle
asked Nov 6, 2017 at 8:25
math.stackexchange.com
12
votes
Prove that $\prod_{1\leq i,j\leq n}\frac{1+a_ia_j}{1-a_ia_j}\geq1$ for $n$ real numbers $a_i\in(-1,1)$
real-analysis
algebra-precalculus
inequality
contest-math
asked Mar 27, 2023 at 7:30
math.stackexchange.com
11
votes
A problem in additive combinatorics
nt.number-theory
cv.complex-variables
inequalities
additive-combinatorics
trigonometric-sums
asked Jul 13, 2020 at 10:13
mathoverflow.net
7
votes
Some Combinatorics and Some Prime Numbers
combinatorics
number-theory
polynomials
prime-numbers
alternative-proof
asked May 14, 2020 at 14:41
math.stackexchange.com
6
votes
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
math.stackexchange.com
5
votes
Applications of Tits' alternative in number theory
number-theory
free-groups
geometric-group-theory
solvable-groups
asked Jul 13, 2020 at 9:41
math.stackexchange.com
5
votes
Why is "The Devil's Backbone" called that?
title
the-devils-backbone
asked Jul 9, 2020 at 17:39
movies.stackexchange.com
1
2
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Top Answers
21
Is it possible that $2^{2A}+2^{2B}$ is a square number?
math.stackexchange.com
20
Book recommendation : Olympiad Combinatorics book
math.stackexchange.com
16
Polynomial outputs containing a particular Integer sequence
math.stackexchange.com
11
When is $-3$ a quadratic residue mod $p$?
math.stackexchange.com
8
Find the roots of all cubics $f(x)$ given $f(2)=1$ and all roots are integral
math.stackexchange.com
6
what points make $\frac{1}{x} + \frac{1}{y} = \frac{1}{n}$ true?
math.stackexchange.com
6
Find all positive integers $n$ such that $\varphi(n)$ divides $n^2 + 3$
math.stackexchange.com
6
INMO : Prove that $\sqrt[3]{a}$ and $\sqrt[3] {b}$ themselves are rational numbers
math.stackexchange.com
5
Some Combinatorics and Some Prime Numbers
math.stackexchange.com
5
If $abc=1$ and $a,b,c$ are positive real numbers, prove that ${1 \over a+b+1} + {1 \over b+c+1} + {1 \over c+a+1} \le 1$.
math.stackexchange.com
5
Does $\Phi_n(\alpha)=0$ in $\Bbb{F}_p$ for some $\alpha\in\mathbb{F}_p$ imply that $\mathrm{ord}_p(\alpha) = n$?
math.stackexchange.com
5
USA TST 2018/P1: Prove that the $n^{\text{th}}$ smallest positive integer relatively prime to $n$ is at least $\sigma(n)$
math.stackexchange.com
5
We have $a,b,c$ and $d$ are real numbers such that $\frac{b + c + d}{a} = \frac{a + c + d}{b} = \frac{a + b + d}{c} = \frac{a + b + c}{d} = r$.
math.stackexchange.com
5
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
math.stackexchange.com
5
Prove that $\sum _{x=0}^{p-1}e^{\frac {2\pi ix^{2}}{p}}={\sqrt {p}} $ , $ p \equiv 1{\pmod {4}}$
math.stackexchange.com
5
How can I prove this inequality using HM-GM-AM-QM inequalities?
math.stackexchange.com