Question

Are there natural number solutions to the equation $a^2(m^3n-n^3m)=b^2(u^3v-v^3u)=c^2(p^3q-q^3p)$ such that the following conditions are met?

score 89 · Answer 1 · 2023-04-04 10:03:40

89

Views

Are there natural number solutions to the equation $a^2(m^3n-n^3m)=b^2(u^3v-v^3u)=c^2(p^3q-q^3p)$ such that the following conditions are met?

Published on 04 Apr 2023 - 10:03

score 141 · Answer 2 · 2026-04-05 04:54:15

Given a positive integer $n$, find all $x$ and $y$ such that $\dfrac1{\sqrt{n}} =\dfrac1{\sqrt{x}}+\dfrac1{\sqrt{y}} $ with $1 \le x \le y$.

score 151 · Answer 3 · 2026-02-23 03:56:13

151

Views

Find integer solutions to $x^2y + xy^2 = 240$

Published on 23 Feb 2026 - 3:56

score 106 · Answer 4 · 2023-04-10 04:01:00

106

Views

Solving the Diophantine equation $xy = az + b$ for $x, y, z \in \mathbb{Z}$

Published on 10 Apr 2023 - 4:01

score 170 · Answer 5 · 2023-04-12 18:48:29

170

Views

Solutions to the Diophantine equation $(ab)(a+b) = N$

Published on 12 Apr 2023 - 18:48

score 82 · Answer 6 · 2026-03-26 09:17:55

82

Views

Rational approximation of $\sqrt[3]{2}$ for the diophantine $x^3 - 2y^3 = 1$

Published on 26 Mar 2026 - 9:17

score 83 · Answer 7 · 2023-04-16 14:27:22

83

Views

Text problem (linear diophantine equation??)

Published on 16 Apr 2023 - 14:27

score 90 · Answer 8 · 2023-04-23 22:13:51

90

Views

Information on the diophantine equation $p^x-q^y=p-q$

Published on 23 Apr 2023 - 22:13

score 100 · Answer 9 · 2023-04-25 01:13:30

100

Views

Integers solutions of modified Markoff equation with parameter $k\in\mathbb{N}$ : $p^2 + q^2 + r^2 = kpqr$

Published on 25 Apr 2023 - 1:13

score 114 · Answer 10 · 2023-04-30 12:32:31

114

Views

Number of unordered pairs $(x,y)$ such that $x^2+3xy+y^2=n$

Published on 30 Apr 2023 - 12:32

score 64 · Answer 11 · 2023-05-01 16:23:31

64

Views

Find all solutions satisfying $|x|+|y|<10 000$ given diophantine equation

Published on 01 May 2023 - 16:23

score 111 · Answer 12 · 2023-05-02 16:34:24

111

Views

A farmer buys $120$ head of livestock for a cost of $8000$

Published on 02 May 2023 - 16:34

score 81 · Answer 13 · 2023-05-04 23:40:51

81

Views

When is $\{x^2+y^k \mod n: x,y \in \mathbb{Z}/n\mathbb{Z}\} \neq \mathbb{Z}/n\mathbb{Z}$?

Published on 04 May 2023 - 23:40

score 56 · Answer 14 · 2023-05-05 17:36:03

56

Views

Another Diophantine word problem.

Published on 05 May 2023 - 17:36

score 153 · Answer 15 · 2026-03-26 13:48:05

153

Views

Does $2y^2=x^4-17$ have solution in $\Bbb{Q}(\sqrt{-3})$?

Published on 26 Mar 2026 - 13:48

List Question

Are there natural number solutions to the equation $a^2(m^3n-n^3m)=b^2(u^3v-v^3u)=c^2(p^3q-q^3p)$ such that the following conditions are met?

Given a positive integer $n$, find all $x$ and $y$ such that $\dfrac1{\sqrt{n}} =\dfrac1{\sqrt{x}}+\dfrac1{\sqrt{y}} $ with $1 \le x \le y$.

Find integer solutions to $x^2y + xy^2 = 240$

Solving the Diophantine equation $xy = az + b$ for $x, y, z \in \mathbb{Z}$

Solutions to the Diophantine equation $(ab)(a+b) = N$

Rational approximation of $\sqrt[3]{2}$ for the diophantine $x^3 - 2y^3 = 1$

Text problem (linear diophantine equation??)

Information on the diophantine equation $p^x-q^y=p-q$

Integers solutions of modified Markoff equation with parameter $k\in\mathbb{N}$ : $p^2 + q^2 + r^2 = kpqr$

Number of unordered pairs $(x,y)$ such that $x^2+3xy+y^2=n$

Find all solutions satisfying $|x|+|y|<10 000$ given diophantine equation

A farmer buys $120$ head of livestock for a cost of $8000$

When is $\{x^2+y^k \mod n: x,y \in \mathbb{Z}/n\mathbb{Z}\} \neq \mathbb{Z}/n\mathbb{Z}$?

Another Diophantine word problem.

Does $2y^2=x^4-17$ have solution in $\Bbb{Q}(\sqrt{-3})$?

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