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 424 · Answer 1 · 2026-03-24 14:49:52

424

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 24 Mar 2026 - 14:49

score 413 · Answer 2 · 2026-03-24 01:14:42

413

Views

monochromatic solution to $xy=z$

Published on 24 Mar 2026 - 1:14

score 93 · Answer 3 · 2019-01-25 17:31:36

93

Views

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

Published on 25 Jan 2019 - 17:31

score 113 · Answer 4 · 2026-03-24 05:08:29

113

Views

Making 12 by adding 1, 3, and 5

Published on 24 Mar 2026 - 5:08

score 30 · Answer 5 · 2026-03-19 22:48:21

30

Views

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

Published on 19 Mar 2026 - 22:48

score 75 · Answer 6 · 2026-03-20 05:53:46

75

Views

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

Published on 20 Mar 2026 - 5:53

score 55 · Answer 7 · 2026-03-23 03:40:38

55

Views

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

Published on 23 Mar 2026 - 3:40

score 137 · Answer 8 · 2026-03-22 23:19:12

137

Views

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

Published on 22 Mar 2026 - 23:19

score 59 · Answer 9 · 2026-03-22 02:17:55

59

Views

Combinatorial problem discrete math

Published on 22 Mar 2026 - 2:17

score 105 · Answer 10 · 2026-03-23 14:29:49

105

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 23 Mar 2026 - 14:29

score 95 · Answer 11 · 2019-03-19 02:53:27

95

Views

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

Published on 19 Mar 2019 - 2:53

score 37 · Answer 12 · 2026-03-24 10:44:37

37

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 24 Mar 2026 - 10:44

score 144 · Answer 13 · 2026-03-24 23:00:42

144

Views

Each one in $\mathbb Z_p$ is some sum

Published on 24 Mar 2026 - 23:00

score 470 · Answer 14 · 2026-03-24 21:43:09

470

Views

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

Published on 24 Mar 2026 - 21:43

score 48 · Answer 15 · 2026-03-24 21:36:56

48

Views

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

Published on 24 Mar 2026 - 21:36

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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