List questions from diophantine-equations

Published on 03 Jul 2020 - 22:57

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Integer solutions to the equation $y^2\pm3xy+x^2=\ell$

Published on 05 Jul 2020 - 0:43

479

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What are all possible positive integers $k$ such that $k=\frac{a^2+b^2+c^2}{bc+ca+ab}$ for some positive integers $a$, $b$, and $c$?

Published on 25 Mar 2026 - 15:42

322

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How do I find the integer solutions that satisfy $xyz = 288$ and $xy + xz + yz = 144$?

Published on 23 Feb 2026 - 3:41

247

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Consider the following Diophantine equation: $x^2 + xy + y^2 = n$

Published on 29 Mar 2026 - 15:35

69

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Parametric solution of a Diophantine equation of three variables

Published on 08 Jul 2020 - 6:04

86

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What is the cardinality of a vanishing set?

Published on 08 Jul 2020 - 11:46

185

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Chevalley–Warning theorem's proof

Published on 08 Jul 2020 - 13:37

142

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Integer solutions of $2a+2b-ab\gt 0$

Published on 08 Jul 2020 - 15:35

187

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System of quadratic homogeneous Diophantine equations

Published on 09 Jul 2020 - 5:17

89

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The general Ramanujan–Nagell equation $x^2+D=y^n$

Published on 09 Jul 2020 - 20:20

190

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How is this set of solutions for exponential diophantine equations been found?(Generalized Collatz mx+1, 2-odd-step-cycle)

Published on 23 Feb 2026 - 4:01

84

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A property of finite fields

Published on 10 Jul 2020 - 14:41

239

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Find out, with no resolution, whether or not the second degree diophantine equations with 2 unknowns have solutions

Published on 10 Jul 2020 - 16:28

506

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No solutions of $x^n+y^n=z^n$ such that $x$, $y$, $z$ are primes

Published on 10 Jul 2020 - 17:05

List Question

The equation $y^2=x\pm \ell $

Integer solutions to the equation $y^2\pm3xy+x^2=\ell$

What are all possible positive integers $k$ such that $k=\frac{a^2+b^2+c^2}{bc+ca+ab}$ for some positive integers $a$, $b$, and $c$?

How do I find the integer solutions that satisfy $xyz = 288$ and $xy + xz + yz = 144$?

Consider the following Diophantine equation: $x^2 + xy + y^2 = n$

Parametric solution of a Diophantine equation of three variables

What is the cardinality of a vanishing set?

Chevalley–Warning theorem's proof

Integer solutions of $2a+2b-ab\gt 0$

System of quadratic homogeneous Diophantine equations

The general Ramanujan–Nagell equation $x^2+D=y^n$

How is this set of solutions for exponential diophantine equations been found?(Generalized Collatz mx+1, 2-odd-step-cycle)

A property of finite fields

Find out, with no resolution, whether or not the second degree diophantine equations with 2 unknowns have solutions

No solutions of $x^n+y^n=z^n$ such that $x$, $y$, $z$ are primes

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