Question

Factorizations versus integer solutions in single-variable quartics

score 61 · Answer 1 · 2026-04-23 14:56:54

61

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Factorizations versus integer solutions in single-variable quartics

Published on 23 Apr 2026 - 14:56

score 103 · Answer 2 · 2026-04-17 08:26:09

103

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The number of the solutions $(x_0,y_0)$ for $x^2+y^2=z_0^2$ such that $(x_0,y_0) \in \mathbb{N} \times \mathbb{N}$

Published on 17 Apr 2026 - 8:26

score 238 · Answer 3 · 2026-04-15 06:26:16

238

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Integer solutions for $\frac{1}{a} + \frac{1}{b}=\frac{p}{q}$

Published on 15 Apr 2026 - 6:26

score 338 · Answer 4 · 2026-04-09 20:02:07

338

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Does the diophantine equation $ax^2+by^2=cz^2+d$ always have solutions?

Published on 09 Apr 2026 - 20:02

score 166 · Answer 5 · 2026-04-13 20:59:28

166

Views

Are $a=3, b=7$ the only solutions to $\sqrt{3}+\sqrt[3]{7}=\sqrt{a}+\sqrt[3]{b}$ for $a,b \in \mathbb{Q}$?

Published on 13 Apr 2026 - 20:59

score 80 · Answer 6 · 2026-04-16 07:37:18

80

Views

Integer solutions to $2^{^{11}} a + 2^{^{11}} b + ab = 1$

Published on 16 Apr 2026 - 7:37

score 631 · Answer 7 · 2026-04-17 12:16:11

631

Views

Does Diophantine equation $1+n+n^2+\dots+n^k=2m^2$ have a solution for $n,k \geq 2$?

Published on 17 Apr 2026 - 12:16

score 101 · Answer 8 · 2026-04-09 04:22:59

101

Views

Can I say the integer solution of this equation is unique?

Published on 09 Apr 2026 - 4:22

score 206 · Answer 9 · 2026-04-13 00:09:01

206

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Does $(n^p-1)/(n-1)=m^2$ have any positive integer solutions for $p\ge 2$ prime?

Published on 13 Apr 2026 - 0:09

score 198 · Answer 10 · 2026-04-09 17:16:54

198

Views

Finding all solutions to quartic Diophantine equation

Published on 09 Apr 2026 - 17:16

score 163 · Answer 11 · 2026-04-12 04:25:54

163

Views

Diophantine equation $ \frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} = n $ computable?

Published on 12 Apr 2026 - 4:25

score 838 · Answer 12 · 2026-04-15 18:06:06

838

Views

Finding formula that solves $w^4+x^4=y^4+z^4$ over the integers.

Published on 15 Apr 2026 - 18:06

score 87 · Answer 13 · 2026-04-14 19:42:07

87

Views

Is $(y,T)=(7,8)$ the only solution in positive integers to $\frac{F(y)}{F(T)}=\frac12$, where $F(x)=x(x-1)(x-2)(x-3)$?

Published on 14 Apr 2026 - 19:42

score 116 · Answer 14 · 2026-04-16 09:38:03

116

Views

No. of solutions of $m^4 = 9n^2 + 72$ where $m$ and $n$ are integers

Published on 16 Apr 2026 - 9:38

score 152 · Answer 15 · 2026-04-12 00:27:03

152

Views

Solveablity of Diophantine equation over "computer numbers"

Published on 12 Apr 2026 - 0:27

List Question

Factorizations versus integer solutions in single-variable quartics

The number of the solutions $(x_0,y_0)$ for $x^2+y^2=z_0^2$ such that $(x_0,y_0) \in \mathbb{N} \times \mathbb{N}$

Integer solutions for $\frac{1}{a} + \frac{1}{b}=\frac{p}{q}$

Does the diophantine equation $ax^2+by^2=cz^2+d$ always have solutions?

Are $a=3, b=7$ the only solutions to $\sqrt{3}+\sqrt[3]{7}=\sqrt{a}+\sqrt[3]{b}$ for $a,b \in \mathbb{Q}$?

Integer solutions to $2^{^{11}} a + 2^{^{11}} b + ab = 1$

Does Diophantine equation $1+n+n^2+\dots+n^k=2m^2$ have a solution for $n,k \geq 2$?

Can I say the integer solution of this equation is unique?

Does $(n^p-1)/(n-1)=m^2$ have any positive integer solutions for $p\ge 2$ prime?

Finding all solutions to quartic Diophantine equation

Diophantine equation $ \frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} = n $ computable?

Finding formula that solves $w^4+x^4=y^4+z^4$ over the integers.

Is $(y,T)=(7,8)$ the only solution in positive integers to $\frac{F(y)}{F(T)}=\frac12$, where $F(x)=x(x-1)(x-2)(x-3)$?

No. of solutions of $m^4 = 9n^2 + 72$ where $m$ and $n$ are integers

Solveablity of Diophantine equation over "computer numbers"

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