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52 votes

Techniques for debugging proofs

answered Apr 29, 2022 at 13:48

26 votes

Accepted

Existence of a zero-sum subset

answered Jan 8, 2021 at 7:32

23 votes

Accepted

Consecutive non-quadratic residues

answered Mar 24, 2014 at 18:25

23 votes

Accepted

All polynomials are the sum of three others, each of which has only real roots

answered Mar 11, 2018 at 10:04

22 votes

Is there a set of positive integers of density 1 which contains no infinite arithmetic progression?

answered Jun 7, 2019 at 12:28

20 votes

Number of vectors so that no two subset sums are equal

answered Feb 15, 2014 at 13:44

19 votes

Accepted

Does small Perron-Frobenius eigenvalue imply small entries for integral matrices?

answered May 9, 2014 at 8:23

18 votes

Accepted

When does $P(a−b)=0$ for $a≠b$ ensure $P(0)=0$? (Continued.)

answered May 17, 2016 at 7:04

17 votes

Accepted

Existence of range of numbers containing a coprime to given n

answered Jul 31, 2016 at 16:39

17 votes

Accepted

sum, integral of certain functions

answered Dec 24, 2016 at 20:36

17 votes

Is there an "analytical" version of Tao's uncertainty principle?

answered Apr 17, 2018 at 13:38

16 votes

How $a+b$ can grow when $a!b! \mid n!$

answered Jul 27, 2013 at 15:11

16 votes

Accepted

The maximal subset of a finite field where the sum of any subset is non-zero

answered Mar 8, 2022 at 7:23

15 votes

Examples of eventual counterexamples

answered May 20, 2011 at 6:37

15 votes

Can you cover the Boolean cube $\{0,1\}^n$ with $O(1)$ Hamming-balls each of radius $n/2-c\sqrt{n}$?

answered Jul 16, 2012 at 10:21

15 votes

Accepted

How are such sets of natural numbers called?

answered Mar 28, 2018 at 6:45

15 votes

Accepted

Multiples in sets of positive upper density

answered Jul 22, 2017 at 9:28

14 votes

Decomposing a finite group as a product of subsets

answered May 28, 2017 at 19:27

14 votes

Accepted

Near-Legendre Conjecture

answered Jan 17, 2019 at 10:00

14 votes

Accepted

Set of integers having finite intersection with the image of any polynomial of degree $\geq 2$

answered Feb 14, 2015 at 21:08

14 votes

Sets that are not sum of subsets

answered Oct 31, 2021 at 7:23

13 votes

How to recognise that the polynomial method might work

answered Oct 25, 2010 at 15:44

12 votes

Sums of powers mod p

answered Apr 1, 2012 at 18:43

12 votes

Accepted

Paths in groups

answered May 16, 2014 at 5:09

12 votes

Accepted

The maximal "nearly convex" function

answered Nov 26, 2013 at 9:11

12 votes

Accepted

Proof of Minkowski theorem using harmonic analysis

answered Sep 18, 2018 at 18:27

12 votes

Accepted

On approximation of $\sum_{a,b=1}^n\gcd(a,b)$

answered Nov 10, 2018 at 9:07

12 votes

On Euler's polynomial $x^2+x+41$

answered Jun 11, 2019 at 16:18

12 votes

Smallest set such that all arithmetic progression will always contain at least a number in a set

answered Jun 27, 2019 at 10:42

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180 Answers

Techniques for debugging proofs

Existence of a zero-sum subset

Consecutive non-quadratic residues

All polynomials are the sum of three others, each of which has only real roots

Is there a set of positive integers of density 1 which contains no infinite arithmetic progression?

Number of vectors so that no two subset sums are equal

Does small Perron-Frobenius eigenvalue imply small entries for integral matrices?

When does $P(a−b)=0$ for $a≠b$ ensure $P(0)=0$? (Continued.)

Existence of range of numbers containing a coprime to given n

sum, integral of certain functions

Is there an "analytical" version of Tao's uncertainty principle?

How $a+b$ can grow when $a!b! \mid n!$

The maximal subset of a finite field where the sum of any subset is non-zero

Examples of eventual counterexamples

Can you cover the Boolean cube $\{0,1\}^n$ with $O(1)$ Hamming-balls each of radius $n/2-c\sqrt{n}$?

How are such sets of natural numbers called?

Multiples in sets of positive upper density

Decomposing a finite group as a product of subsets

Near-Legendre Conjecture

Set of integers having finite intersection with the image of any polynomial of degree $\geq 2$

Sets that are not sum of subsets

More open problems

How to recognise that the polynomial method might work

Sums of powers mod p

Paths in groups

The maximal "nearly convex" function

Proof of Minkowski theorem using harmonic analysis

On approximation of $\sum_{a,b=1}^n\gcd(a,b)$

On Euler's polynomial $x^2+x+41$

Smallest set such that all arithmetic progression will always contain at least a number in a set