User Roland Bacher

52 votes

24 answers

10k views

Most elementary proof showing that exponential growth wins against polynomial growth

asked Nov 5, 2023 at 14:11

43 votes

12 answers

2k views

Can a discrete set of the plane of uniform density intersect all large triangles?

asked Oct 29, 2009 at 18:16

42 votes

2 answers

2k views

A curious identity related to finite fields

asked Feb 26, 2014 at 16:40

39 votes

3 answers

6k views

A limit involving binomial coefficients: $\lim_{n\to\infty} (-1)^n\sum_{k=1}^n(-1)^k{n\choose k}^{-1/k}=\frac12$?

asked Feb 2, 2012 at 18:31

38 votes

5 answers

3k views

An explicit example of a finitely presented group containing a subgroup isomorphic to $(\mathbb Q,+)$.

asked May 3, 2010 at 16:38

31 votes

6 answers

2k views

Useful tricks in experimental mathematics

asked May 15, 2011 at 12:02

31 votes

3 answers

1k views

Which power series have bounded integral coefficients and have an inverse given by a series having bounded integral coefficients

asked Feb 16, 2015 at 17:16

29 votes

1 answer

2k views

Reason for breakdown of a nice binomial identity

asked Aug 3, 2022 at 14:39

25 votes

1 answer

905 views

Reference request for a proof of the two-square Theorem

asked Oct 5, 2021 at 12:02

24 votes

2 answers

9k views

Explanation why $x,y,z$ are always variables

asked Jul 2, 2010 at 13:37

21 votes

1 answer

581 views

Existence of a polynomial $Q$ of degree $\geq (p-1)/4$ in $\mathbb F_p[x]$ such that $QQ'$ factorizes into distinct linear factors

asked Aug 21, 2021 at 13:23

20 votes

3 answers

1k views

Size of set of integers with all sums of two distinct elements giving squares

asked Nov 11, 2021 at 21:14

20 votes

0 answers

666 views

Polynomials with roots in convex position

asked Jun 2, 2010 at 8:21

20 votes

8 answers

14k views

"Natural" generating sets for symmetric groups

asked May 10, 2010 at 13:52

19 votes

3 answers

2k views

Cutting convex sets

asked May 12, 2010 at 9:03

19 votes

2 answers

2k views

Constants for Rolle's Theorem applied to polynomials

asked Nov 2, 2011 at 18:25

18 votes

5 answers

7k views

Is $x^p-x+1$ always irreducible in $\mathbb F_p[x]$?

asked May 19, 2014 at 15:40

18 votes

0 answers

370 views

Colouring Gaussian integers according to a numeral system based on powers of $-1+i$

asked Nov 6, 2022 at 20:47

17 votes

4 answers

1k views

Are there natural choices of $\sqrt{-1}$ in $\mathbb Z/p\mathbb Z$ for a prime $p\equiv 1\pmod 4$

asked Jun 21, 2010 at 14:27

16 votes

5 answers

1k views

Name of a polytope

asked Mar 31, 2011 at 9:11

15 votes

7 answers

2k views

An Erdős-Szekeres-type question

asked Jun 14, 2011 at 13:56

15 votes

1 answer

947 views

Procreation with several genders

asked May 11, 2010 at 15:59

15 votes

2 answers

1k views

Asymptotic approximation of $x^\alpha$ by entire functions

asked May 28, 2010 at 8:56

15 votes

2 answers

306 views

Convergency radius of the generating series for A93637

asked Oct 13, 2022 at 17:59

15 votes

2 answers

827 views

Are there exotic polynomial bijections from $\mathbb N^d$ onto $\mathbb N$?

asked Aug 4, 2021 at 21:38

14 votes

0 answers

294 views

An 'onion-structure' for roots of a series associated to prime numbers?

asked Jan 4, 2023 at 22:06

13 votes

1 answer

577 views

A congruence for a product of binomial coefficients?

asked Dec 29, 2022 at 18:40

13 votes

0 answers

217 views

A game based on the Euclidean algorithm

asked Aug 14, 2021 at 21:54

13 votes

1 answer

327 views

Spectral properties of finite metric sets

asked Feb 16, 2011 at 14:21

13 votes

2 answers

1k views

An unfair game involving an odd number of pieces of chocolate

asked Apr 10, 2013 at 17:04

Stack Exchange Network

143 Questions

Most elementary proof showing that exponential growth wins against polynomial growth

Can a discrete set of the plane of uniform density intersect all large triangles?

A curious identity related to finite fields

A limit involving binomial coefficients: $\lim_{n\to\infty} (-1)^n\sum_{k=1}^n(-1)^k{n\choose k}^{-1/k}=\frac12$?

An explicit example of a finitely presented group containing a subgroup isomorphic to $(\mathbb Q,+)$.

Useful tricks in experimental mathematics

Which power series have bounded integral coefficients and have an inverse given by a series having bounded integral coefficients

Reason for breakdown of a nice binomial identity

Reference request for a proof of the two-square Theorem

Explanation why $x,y,z$ are always variables

Existence of a polynomial $Q$ of degree $\geq (p-1)/4$ in $\mathbb F_p[x]$ such that $QQ'$ factorizes into distinct linear factors

Size of set of integers with all sums of two distinct elements giving squares

Polynomials with roots in convex position

"Natural" generating sets for symmetric groups

Cutting convex sets

Constants for Rolle's Theorem applied to polynomials

Is $x^p-x+1$ always irreducible in $\mathbb F_p[x]$?

Colouring Gaussian integers according to a numeral system based on powers of $-1+i$

Are there natural choices of $\sqrt{-1}$ in $\mathbb Z/p\mathbb Z$ for a prime $p\equiv 1\pmod 4$

Name of a polytope

An Erdős-Szekeres-type question

Procreation with several genders

Asymptotic approximation of $x^\alpha$ by entire functions

Convergency radius of the generating series for A93637

Are there exotic polynomial bijections from $\mathbb N^d$ onto $\mathbb N$?

An 'onion-structure' for roots of a series associated to prime numbers?

A congruence for a product of binomial coefficients?

A game based on the Euclidean algorithm

Spectral properties of finite metric sets

An unfair game involving an odd number of pieces of chocolate