List questions from diophantine-equations

Published on 12 Apr 2026 - 1:13

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Equation in integers $x y^2 + 2 y z^2 + z x^2 = 0$

Published on 14 Apr 2026 - 21:15

167

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Is there any solution to this Diophantine equation?

Published on 13 Apr 2026 - 16:05

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Can $x^2+y$ and $y^2+x$ both be perfect squares for $x,y$ positive integers?

Published on 16 Apr 2026 - 13:15

65

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Solving two equations with four variables over integers

Published on 15 Apr 2026 - 11:29

190

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About the diophantine equation $x^3+y^3=z^8$

Published on 14 Apr 2026 - 16:48

130

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How to solve the Diophantine equation $x^4 + 2x^3 -3x^2-4x-y^2-2y-6=0$?

Published on 24 Apr 2026 - 7:03

151

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Generalized Pell's equation where $N$ is perfect square

Published on 16 Apr 2026 - 1:36

73

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Positive integral solutions $(m,n)$ to $m = n^m$

Published on 16 Apr 2026 - 5:21

683

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Finding integer solutions to $(x-y)^2+(y-z)^2+(z-x)^2=2022$

Published on 24 Apr 2026 - 5:18

122

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For a given integer $n>0$, can we efficiently determine whether an integer $y$ exist such that $n+y^2$ is a perfect square?

Published on 14 Apr 2026 - 18:10

121

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For a perfect square $n$, can we calculate integers $0<y<l$ up to a limit $l$ such that $n+y^2$ is a perfect square (without bruteforce)?

Published on 14 Apr 2026 - 17:23

185

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Proof of $a^3 - b^3 = c^3 + d^3$, where $a,b,c,d$ all rational?

Published on 14 Apr 2026 - 19:00

118

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Diophant/prime equation $p(p-1) = 2(n^3 + 1)$ where $p$ is prime, and $n$ can be $0$

Published on 15 Apr 2026 - 19:24

87

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Area of Triangle and Diophantine Equations

Published on 15 Apr 2026 - 10:54

List Question

Situations in which new information is irrelevant in conditional probability

Equation in integers $x y^2 + 2 y z^2 + z x^2 = 0$

Is there any solution to this Diophantine equation?

Can $x^2+y$ and $y^2+x$ both be perfect squares for $x,y$ positive integers?

Solving two equations with four variables over integers

About the diophantine equation $x^3+y^3=z^8$

How to solve the Diophantine equation $x^4 + 2x^3 -3x^2-4x-y^2-2y-6=0$?

Generalized Pell's equation where $N$ is perfect square

Positive integral solutions $(m,n)$ to $m = n^m$

Finding integer solutions to $(x-y)^2+(y-z)^2+(z-x)^2=2022$

For a given integer $n>0$, can we efficiently determine whether an integer $y$ exist such that $n+y^2$ is a perfect square?

For a perfect square $n$, can we calculate integers $0<y<l$ up to a limit $l$ such that $n+y^2$ is a perfect square (without bruteforce)?

Proof of $a^3 - b^3 = c^3 + d^3$, where $a,b,c,d$ all rational?

Diophant/prime equation $p(p-1) = 2(n^3 + 1)$ where $p$ is prime, and $n$ can be $0$

Area of Triangle and Diophantine Equations

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