List questions from diophantine-equations

Published on 15 Feb 2018 - 13:50

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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 15 Feb 2018 - 15:48

1.6k

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Existence of Solution to Generalized Pell's Equation

Published on 22 Mar 2026 - 10:14

603

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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 25 Mar 2026 - 3:04

72

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

Published on 25 Mar 2026 - 3:19

329

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Diophantine equations with irrational coefficients

Published on 20 Mar 2026 - 2:56

487

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Problem of Mary Somerville and Hypatia

Published on 25 Mar 2026 - 4:10

894

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Irregular polygons with non-equal integer side lengths and diagonals

Published on 24 Mar 2026 - 20:31

70

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Do integer right-angled tetrahedra exist?

Published on 19 Feb 2018 - 5:17

654

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A hard Cubic Diophantine equation

Published on 19 Feb 2018 - 12:51

5.6k

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Pythagorean triples that "survive" Euler's totient function

Published on 25 Mar 2026 - 6:18

310

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

Published on 21 Feb 2018 - 4:43

58

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Problem with Diophantine equations

Published on 21 Feb 2018 - 11:43

89

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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 22 Feb 2018 - 15:00

525

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

Published on 23 Feb 2018 - 18:21

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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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