Question

How to show that $\gcd(a_1,a_2,\cdots,a_k) = 1$ implies that there exist a non-negative solution to $\sum_{i=1}^{n}a_ix_i = n$ for large $n.$

score 430 · Answer 1 · 2026-05-16 01:36:03

430

Views

How to show that $\gcd(a_1,a_2,\cdots,a_k) = 1$ implies that there exist a non-negative solution to $\sum_{i=1}^{n}a_ix_i = n$ for large $n.$

Published on 16 May 2026 - 1:36

score 206 · Answer 2 · 2026-05-10 15:30:16

206

Views

On Yanqi Xu's 2016 joint undergraduate math research project with Dr. Judy Holdener at Kenyon College

Published on 10 May 2026 - 15:30

score 137 · Answer 3 · 2026-05-11 00:30:55

137

Views

Special cases of Szemeredi's Theorem?

Published on 11 May 2026 - 0:30

score 87 · Answer 4 · 2026-04-17 07:04:15

87

Views

Any good way to calculate $\frac {\alpha ^ n - 1 } {\alpha - 1} \pmod{c}$

Published on 17 Apr 2026 - 7:04

score 79 · Answer 5 · 2026-04-14 21:45:54

79

Views

irreducible polynomial has all its roots in $F_s$ and every element in $F_s$ satisfies such a polynomial

Published on 14 Apr 2026 - 21:45

score 350 · Answer 6 · 2026-05-10 21:59:03

350

Views

Understanding Graham's proof of theorem on Unit Fractions.

Published on 10 May 2026 - 21:59

score 154 · Answer 7 · 2026-05-15 10:00:06

154

Views

On $\sup|\varphi^{-1}(n)|=+\infty$

Published on 15 May 2026 - 10:00

score 49 · Answer 8 · 2026-05-10 15:49:59

49

Views

Diophantine Approximation on Quadratic Polynomials

Published on 10 May 2026 - 15:49

score 29 · Answer 9 · 2026-04-16 07:55:28

29

Views

Given two positive integer numbers m,n, show that m/n can't have period b−1 in base b.

Published on 16 Apr 2026 - 7:55

score 171 · Answer 10 · 2026-05-14 22:53:13

171

Views

Combinations of red and black balls

Published on 14 May 2026 - 22:53

score 160 · Answer 11 · 2026-04-11 09:23:13

160

Views

A question about the number 541456

Published on 11 Apr 2026 - 9:23

score 43 · Answer 12 · 2026-04-16 11:08:15

43

Views

For $1\leq a\leq p-1$ and $5\leq p$, show that $\sum_{(a/p)=1}^{} a \equiv 0 \pmod{p}$

Published on 16 Apr 2026 - 11:08

score 914 · Answer 13 · 2026-04-15 12:27:41

Is it possible to represent $e=2.71\ldots$ and $\pi=3.14\ldots$ algebraicially, without using infinity or infinitely-many numbers?

score 671 · Answer 14 · 2026-05-15 00:41:52

671

Views

On the definition of Liouville number

Published on 15 May 2026 - 0:41

score 1.2k · Answer 15 · 2026-04-11 12:28:21

1.2k

Views

Primes in $\mathbb{Z}[\sqrt{2}]$?

Published on 11 Apr 2026 - 12:28

List Question

How to show that $\gcd(a_1,a_2,\cdots,a_k) = 1$ implies that there exist a non-negative solution to $\sum_{i=1}^{n}a_ix_i = n$ for large $n.$

On Yanqi Xu's 2016 joint undergraduate math research project with Dr. Judy Holdener at Kenyon College

Special cases of Szemeredi's Theorem?

Any good way to calculate $\frac {\alpha ^ n - 1 } {\alpha - 1} \pmod{c}$

irreducible polynomial has all its roots in $F_s$ and every element in $F_s$ satisfies such a polynomial

Understanding Graham's proof of theorem on Unit Fractions.

On $\sup|\varphi^{-1}(n)|=+\infty$

Diophantine Approximation on Quadratic Polynomials

Given two positive integer numbers m,n, show that m/n can't have period b−1 in base b.

Combinations of red and black balls

A question about the number 541456

For $1\leq a\leq p-1$ and $5\leq p$, show that $\sum_{(a/p)=1}^{} a \equiv 0 \pmod{p}$

Is it possible to represent $e=2.71\ldots$ and $\pi=3.14\ldots$ algebraicially, without using infinity or infinitely-many numbers?

On the definition of Liouville number

Primes in $\mathbb{Z}[\sqrt{2}]$?

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