Question

Given $p, m$, how many $r, k$ exist such that $\sum_{i=0}^k{m+i \choose p} = {m+r \choose p}$?

score 167 · Answer 1 · 2026-04-17 01:39:26

167

Views

Given $p, m$, how many $r, k$ exist such that $\sum_{i=0}^k{m+i \choose p} = {m+r \choose p}$?

Published on 17 Apr 2026 - 1:39

score 88 · Answer 2 · 2026-04-15 03:36:15

88

Views

Diophantine equation and cyclicity of $\mathbb{F}_p^*$

Published on 15 Apr 2026 - 3:36

score 139 · Answer 3 · 2026-04-14 14:25:00

139

Views

algebraic geometry and elliptic curves

Published on 14 Apr 2026 - 14:25

score 173 · Answer 4 · 2026-04-16 10:47:22

173

Views

Find positive integer that can't be expressed by $\lfloor x/2 \rfloor + y + xy$

Published on 16 Apr 2026 - 10:47

score 577 · Answer 5 · 2026-04-09 02:29:16

577

Views

Unique Integer solution of a non-linear equation

Published on 09 Apr 2026 - 2:29

score 230 · Answer 6 · 2026-04-15 22:31:14

230

Views

If $x,y,z \in \mathbb{Z}$ such that $x^4+y^4+z^4 \equiv 0 \pmod{29}$, prove that $x^4+y^4+z^4 \equiv 0 \pmod{29^4}$

Published on 15 Apr 2026 - 22:31

score 349 · Answer 7 · 2026-04-11 16:45:54

349

Views

Number theory problem, 3rd degree diophantine equation

Published on 11 Apr 2026 - 16:45

score 69 · Answer 8 · 2026-04-14 14:18:45

69

Views

A diophantine definition of the Kleene star

Published on 14 Apr 2026 - 14:18

score 7.6k · Answer 9 · 2026-04-10 20:54:22

7.6k

Views

What are real life applications of Diophantine equations?

Published on 10 Apr 2026 - 20:54

score 155 · Answer 10 · 2026-04-15 16:13:28

155

Views

4-dim. generalization of $ab+ac+bc=0$

Published on 15 Apr 2026 - 16:13

score 135 · Answer 11 · 2026-04-17 09:45:53

135

Views

Prove $\forall a,b,k \in \Bbb Z^+$ such that $a \equiv -1 \bmod 3$ and $b \equiv 1 \bmod 3$, $2^{2k-1}a,2^{2k}b$ are non-trivial polygonal numbers

Published on 17 Apr 2026 - 9:45

score 63 · Answer 12 · 2026-04-10 17:04:25

63

Views

How to solve parameters given 3 different types of information?

Published on 10 Apr 2026 - 17:04

score 3k · Answer 13 · 2026-04-16 14:24:26

3k

Views

Find all integer solutions to Diophantine equation $x^3+y^3+z^3=w^3$

Published on 16 Apr 2026 - 14:24

score 337 · Answer 14 · 2026-04-12 21:25:03

337

Views

Prove that there are exactly 16 solutions to this problem.

Published on 12 Apr 2026 - 21:25

score 783 · Answer 15 · 2026-04-10 08:22:38

783

Views

Linear equation with prime coefficient.

Published on 10 Apr 2026 - 8:22

List Question

Given $p, m$, how many $r, k$ exist such that $\sum_{i=0}^k{m+i \choose p} = {m+r \choose p}$?

Diophantine equation and cyclicity of $\mathbb{F}_p^*$

algebraic geometry and elliptic curves

Find positive integer that can't be expressed by $\lfloor x/2 \rfloor + y + xy$

Unique Integer solution of a non-linear equation

If $x,y,z \in \mathbb{Z}$ such that $x^4+y^4+z^4 \equiv 0 \pmod{29}$, prove that $x^4+y^4+z^4 \equiv 0 \pmod{29^4}$

Number theory problem, 3rd degree diophantine equation

A diophantine definition of the Kleene star

What are real life applications of Diophantine equations?

4-dim. generalization of $ab+ac+bc=0$

Prove $\forall a,b,k \in \Bbb Z^+$ such that $a \equiv -1 \bmod 3$ and $b \equiv 1 \bmod 3$, $2^{2k-1}a,2^{2k}b$ are non-trivial polygonal numbers

How to solve parameters given 3 different types of information?

Find all integer solutions to Diophantine equation $x^3+y^3+z^3=w^3$

Prove that there are exactly 16 solutions to this problem.

Linear equation with prime coefficient.

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