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 426 · Answer 1 · 2026-03-25 08:58:54

426

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 25 Mar 2026 - 8:58

score 417 · Answer 2 · 2026-04-11 02:09:48

417

Views

monochromatic solution to $xy=z$

Published on 11 Apr 2026 - 2:09

score 96 · Answer 3 · 2026-04-14 10:07:19

96

Views

Lemma 2.1 of "A SUM-PRODUCT ESTIMATE IN FINITE FIELDS, AND APPLICATION", by Bourgain, Katz and Tao

Published on 14 Apr 2026 - 10:07

score 116 · Answer 4 · 2026-03-27 05:59:35

116

Views

Making 12 by adding 1, 3, and 5

Published on 27 Mar 2026 - 5:59

score 41 · Answer 5 · 2026-05-07 16:55:25

41

Views

Lower-bounding the density of 3A in terms of that of 2A

Published on 07 May 2026 - 16:55

score 79 · Answer 6 · 2026-04-29 12:24:32

79

Views

Prove that if $|A+A| \leq K|A|$ then $2A - 2A$ is a $K^{16}$-approximate group.

Published on 29 Apr 2026 - 12:24

score 59 · Answer 7 · 2026-04-29 12:24:35

59

Views

Subsets of $\mathbb Z/n\mathbb Z$ that remain disjoint with themselves under shifts

Published on 29 Apr 2026 - 12:24

score 141 · Answer 8 · 2026-04-29 12:24:38

141

Views

Subsets of $\mathbb Z/n\mathbb Z$ disjoint with some of its shifts

Published on 29 Apr 2026 - 12:24

score 62 · Answer 9 · 2026-05-10 14:45:44

62

Views

Combinatorial problem discrete math

Published on 10 May 2026 - 14:45

score 109 · Answer 10 · 2026-04-29 12:24:32

109

Views

Show that there exists $i\in \lbrace 1, 2, 3 \rbrace $ s.t. there exists $a, b\in A_i $ s.t. $a+b\in B $.

Published on 29 Apr 2026 - 12:24

score 97 · Answer 11 · 2026-05-10 15:08:59

97

Views

Reaching higher even numbers in Goldbach's conjecture, using lower even numbers.

Published on 10 May 2026 - 15:08

score 39 · Answer 12 · 2026-03-25 10:30:57

39

Views

On the cardinality of the set $ A(m) := \{ (a, b) \in \mathbb{N}^2 : \; N \leq a \leq 2 N, \; a^2 - b^2 = m \}, $

Published on 25 Mar 2026 - 10:30

score 145 · Answer 13 · 2026-03-25 04:38:29

145

Views

Each one in $\mathbb Z_p$ is some sum

Published on 25 Mar 2026 - 4:38

score 471 · Answer 14 · 2026-03-25 03:03:41

471

Views

Number of n-tuples in $\{0, 1, 2\}$ with sum less than or equal to $d$.

Published on 25 Mar 2026 - 3:03

score 49 · Answer 15 · 2026-03-25 03:07:28

49

Views

If $P \in V$ is a polynomial with maximal support $\Sigma$, then $|\Sigma| \geq dim(V)$

Published on 25 Mar 2026 - 3:07

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 $n.$

monochromatic solution to $xy=z$

Lemma 2.1 of "A SUM-PRODUCT ESTIMATE IN FINITE FIELDS, AND APPLICATION", by Bourgain, Katz and Tao

Making 12 by adding 1, 3, and 5

Lower-bounding the density of 3A in terms of that of 2A

Prove that if $|A+A| \leq K|A|$ then $2A - 2A$ is a $K^{16}$-approximate group.

Subsets of $\mathbb Z/n\mathbb Z$ that remain disjoint with themselves under shifts

Subsets of $\mathbb Z/n\mathbb Z$ disjoint with some of its shifts

Combinatorial problem discrete math

Show that there exists $i\in \lbrace 1, 2, 3 \rbrace $ s.t. there exists $a, b\in A_i $ s.t. $a+b\in B $.

Reaching higher even numbers in Goldbach's conjecture, using lower even numbers.

On the cardinality of the set $ A(m) := \{ (a, b) \in \mathbb{N}^2 : \; N \leq a \leq 2 N, \; a^2 - b^2 = m \}, $

Each one in $\mathbb Z_p$ is some sum

Number of n-tuples in $\{0, 1, 2\}$ with sum less than or equal to $d$.

If $P \in V$ is a polynomial with maximal support $\Sigma$, then $|\Sigma| \geq dim(V)$

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