Question

How to solve $(2k+1)(2k^2+1) = y^2$ over the positive integers

score 268 · Answer 1 · 2026-04-16 12:53:15

268

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How to solve $(2k+1)(2k^2+1) = y^2$ over the positive integers

Published on 16 Apr 2026 - 12:53

score 277 · Answer 2 · 2026-04-12 22:05:17

277

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Solving a Complex Diophantine Equation with One Known

Published on 12 Apr 2026 - 22:05

score 101 · Answer 3 · 2026-04-16 11:01:05

101

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For which positive integer $n$, is $\frac{2^n-1}{3}$ a factor of $4m^2+1$ for some integer $m$? (How to prove that one answer group is the only one?)

Published on 16 Apr 2026 - 11:01

score 192 · Answer 4 · 2026-04-11 12:21:07

192

Views

Only solution to Diophantine equation with primes?

Published on 11 Apr 2026 - 12:21

score 219 · Answer 5 · 2026-04-08 19:45:03

219

Views

Understanding formula to find all solutions of a linear congruence in $\mathbb Z_n$

Published on 08 Apr 2026 - 19:45

score 124 · Answer 6 · 2026-04-24 17:37:25

124

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Number of solutions of $ax+by+cz=n$ in nonnegative integers

Published on 24 Apr 2026 - 17:37

score 41 · Answer 7 · 2026-04-12 06:03:14

41

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The equation $ax+bu+cs=ayz+bvw+crt$ also has no integers solutions for any integers $a,b,c$

Published on 12 Apr 2026 - 6:03

score 73 · Answer 8 · 2026-04-15 09:17:24

Solutions of $\frac{\lfloor \sqrt{n}\rfloor(1 + \lfloor\sqrt{n}\rfloor)}{2 n} = \frac{\lfloor \sqrt{k}\rfloor(1 + \lfloor\sqrt{k}\rfloor)}{2 k}$

score 292 · Answer 9 · 2026-04-16 02:24:50

292

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If a binary quadratic form primitively represents $n$ and $n^3$, must it be the identity form?

Published on 16 Apr 2026 - 2:24

score 315 · Answer 10 · 2026-04-15 20:07:55

315

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A caboodle of Pell's equation in one? $x^2+y^2-5xy+5=0$

Published on 15 Apr 2026 - 20:07

score 55 · Answer 11 · 2026-04-08 11:00:56

55

Views

Does the formulation of a proof involve substitution of numerical solutions into the problem?

Published on 08 Apr 2026 - 11:00

score 96 · Answer 12 · 2026-04-14 22:11:41

96

Views

How many integer points are contained within a cube's intersection with plane?

Published on 14 Apr 2026 - 22:11

score 504 · Answer 13 · 2026-04-15 19:48:27

504

Views

Find all positive integers $x$ such that $x(x+2021)$ is a perfect square

Published on 15 Apr 2026 - 19:48

score 70 · Answer 14 · 2026-04-17 02:12:04

70

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Historical context of the quadruple $(x,y,z,t)$ where $x^2+y^2=z^2+t^2$

Published on 17 Apr 2026 - 2:12

score 104 · Answer 15 · 2026-04-14 00:31:17

104

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Is it possible to solve $\frac{x(x-1)}{(x+y)(x+y-1)} =\frac12$, with $x>y$ and $100 \leq x+y\leq500$, without writing some program?

Published on 14 Apr 2026 - 0:31

List Question

How to solve $(2k+1)(2k^2+1) = y^2$ over the positive integers

Solving a Complex Diophantine Equation with One Known

For which positive integer $n$, is $\frac{2^n-1}{3}$ a factor of $4m^2+1$ for some integer $m$? (How to prove that one answer group is the only one?)

Only solution to Diophantine equation with primes?

Understanding formula to find all solutions of a linear congruence in $\mathbb Z_n$

Number of solutions of $ax+by+cz=n$ in nonnegative integers

The equation $ax+bu+cs=ayz+bvw+crt$ also has no integers solutions for any integers $a,b,c$

Solutions of $\frac{\lfloor \sqrt{n}\rfloor(1 + \lfloor\sqrt{n}\rfloor)}{2 n} = \frac{\lfloor \sqrt{k}\rfloor(1 + \lfloor\sqrt{k}\rfloor)}{2 k}$

If a binary quadratic form primitively represents $n$ and $n^3$, must it be the identity form?

A caboodle of Pell's equation in one? $x^2+y^2-5xy+5=0$

Does the formulation of a proof involve substitution of numerical solutions into the problem?

How many integer points are contained within a cube's intersection with plane?

Find all positive integers $x$ such that $x(x+2021)$ is a perfect square

Historical context of the quadruple $(x,y,z,t)$ where $x^2+y^2=z^2+t^2$

Is it possible to solve $\frac{x(x-1)}{(x+y)(x+y-1)} =\frac12$, with $x>y$ and $100 \leq x+y\leq500$, without writing some program?

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