List questions from diophantine-equations

Published on 14 Sep 2019 - 1:23

252

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If an integer is not sum of two cubes in integers, then the integer cannot be sum of two cubes modulo every integer.

Published on 17 Sep 2019 - 2:15

132

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3 as a sum of three integer cubes

Published on 18 Sep 2019 - 9:41

133

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Solve diophantine equation $x^2+y^2=2(x+y)+xy$

Published on 19 Sep 2019 - 17:15

44

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Diophantine Inequality $4ax - y^2 + z <0$

Published on 19 Sep 2019 - 21:59

70

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Is there any prime number $a$ satisfying $a=\frac{k_1-k_2}{k_1-bk_2}$?

Published on 20 Sep 2019 - 7:50

186

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$ab+ac+bc \equiv 1 \bmod abc$ or "easy chinese remainder theorem problems"

Published on 25 Mar 2026 - 21:49

73

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Is there an example for the Greenleaf theorem?

Published on 25 Mar 2026 - 1:15

190

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Find all $n$ for which $3n^2+3n+1$ is a perfect square.

Published on 28 Mar 2026 - 12:02

1.4k

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Show that $3x^4+4y^4=19z^4$ has no integer solution

Published on 25 Mar 2026 - 12:46

145

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Diophantine equation from the Latvian Baltic Way team selection competition 2019

Published on 26 Sep 2019 - 11:28

193

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Solutions to the Diophantine equation

Published on 27 Sep 2019 - 11:54

857

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Find all pairs of integers $(x,y)$ such that $x^{2}+y^{2}=(x-y)^{3}$.

Published on 29 Sep 2019 - 11:10

300

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Solution to $x^2-y^{11}=23$ in positive integers?

Published on 30 Sep 2019 - 21:41

86

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A Pythagorean quadruple-like equation: $(2a^2)^2+(ab)^2+2^2=c^2$

Published on 01 Oct 2019 - 22:29

List Question

How to check if $ x^2 + x = y^2 - 1$ has positive integer solutions?

If an integer is not sum of two cubes in integers, then the integer cannot be sum of two cubes modulo every integer.

3 as a sum of three integer cubes

Solve diophantine equation $x^2+y^2=2(x+y)+xy$

Diophantine Inequality $4ax - y^2 + z <0$

Is there any prime number $a$ satisfying $a=\frac{k_1-k_2}{k_1-bk_2}$?

$ab+ac+bc \equiv 1 \bmod abc$ or "easy chinese remainder theorem problems"

Is there an example for the Greenleaf theorem?

Find all $n$ for which $3n^2+3n+1$ is a perfect square.

Show that $3x^4+4y^4=19z^4$ has no integer solution

Diophantine equation from the Latvian Baltic Way team selection competition 2019

Solutions to the Diophantine equation

Find all pairs of integers $(x,y)$ such that $x^{2}+y^{2}=(x-y)^{3}$.

Solution to $x^2-y^{11}=23$ in positive integers?

A Pythagorean quadruple-like equation: $(2a^2)^2+(ab)^2+2^2=c^2$

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