List questions from diophantine-equations

Published on 14 Apr 2026 - 1:18

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Conjecture: $N=x_1^2+x_2^2-y^3$ has integer solutions for all $N$, with $x_1>0$,$x_2>0$ and $y>0$

Published on 07 Apr 2026 - 4:31

1.6k

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Existence of Solution to Generalized Pell's Equation

Published on 24 Apr 2026 - 15:03

605

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Show that the tangent to $y^2=x^3-2$ at the "obvious" rational point (3,5) is $y=\frac{27x}{10}-\frac{31}{10}$ using the Diophantus chord method.

Published on 17 Apr 2026 - 3:57

74

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Prove: If $ (a^2 \mid (2b^2))$, then $ (a \mid b). $

Published on 11 Apr 2026 - 20:24

339

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Diophantine equations with irrational coefficients

Published on 27 Apr 2026 - 18:34

490

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Problem of Mary Somerville and Hypatia

Published on 29 Apr 2026 - 12:51

901

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Irregular polygons with non-equal integer side lengths and diagonals

Published on 10 May 2026 - 12:31

73

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Do integer right-angled tetrahedra exist?

Published on 14 Apr 2026 - 12:49

658

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A hard Cubic Diophantine equation

Published on 15 Apr 2026 - 16:15

5.6k

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Pythagorean triples that "survive" Euler's totient function

Published on 10 May 2026 - 13:45

313

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Find all integer solutions to the equation $x^2 − x = y^5 − y$.

Published on 15 Apr 2026 - 20:11

63

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Problem with Diophantine equations

Published on 12 Apr 2026 - 5:16

92

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Finding the smallest integer solution to $N=x_1^2+x_2^2-y^3$ for any given $N$, with $x_1>0$, $x_2>0$ and $y>0$

Published on 15 Apr 2026 - 22:42

528

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Diophantine Equation $a^6+b^6+c^6=d^6$

Published on 13 Apr 2026 - 17:58

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Conjecture: $N=x_1^2+x_2^2-y^3$ has integer solutions for all $N$, with $x_1>0$,$x_2>0$ and $y>0$

Existence of Solution to Generalized Pell's Equation

Show that the tangent to $y^2=x^3-2$ at the "obvious" rational point (3,5) is $y=\frac{27x}{10}-\frac{31}{10}$ using the Diophantus chord method.

Prove: If $ (a^2 \mid (2b^2))$, then $ (a \mid b). $

Diophantine equations with irrational coefficients

Problem of Mary Somerville and Hypatia

Irregular polygons with non-equal integer side lengths and diagonals

Do integer right-angled tetrahedra exist?

A hard Cubic Diophantine equation

Pythagorean triples that "survive" Euler's totient function

Find all integer solutions to the equation $x^2 − x = y^5 − y$.

Problem with Diophantine equations

Finding the smallest integer solution to $N=x_1^2+x_2^2-y^3$ for any given $N$, with $x_1>0$, $x_2>0$ and $y>0$

Diophantine Equation $a^6+b^6+c^6=d^6$

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