List questions from diophantine-equations

Published on 02 Nov 2019 - 7:20

121

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$3(1^2+2^2+...+n^2)$ is a square

Published on 03 Nov 2019 - 9:10

191

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Coincidence in Diophantine solution parametrization for Pythagorean triples etc

Published on 26 Mar 2026 - 12:45

85

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Nonlinear polynomial Diophantine equations

Published on 05 Nov 2019 - 8:32

216

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Show that $2^n+3^n+5^n+6^n$ isn't a perfect cube, for all $n \in \mathbb{N}$.

Published on 27 Mar 2026 - 18:09

987

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When is the number of areas obtained by cutting a circle with $n$ chords a power of $2$?

Published on 06 Nov 2019 - 23:22

190

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Conjecture: any two sequences of polygonal numbers will share multiple terms between them

Published on 07 Nov 2019 - 20:01

102

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Fermat's Last Theorem for even indices

Published on 08 Nov 2019 - 9:15

86

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Does this equation have a solution in the integers: $4^n= \dfrac{x^2+y^2+z^2+w^2}{2}$?

Published on 10 Nov 2019 - 8:37

184

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Quartic equation $x^4-y^4=2$ over rationals

Published on 29 Mar 2026 - 23:58

100

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If $3\omega^2-2n\omega\psi+\psi^2+1=0$ has a rational solution then it has an integer solution?

Published on 27 Feb 2026 - 23:47

73

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Solve quadratic equation with condition that solution should be integer.

Published on 13 Nov 2019 - 9:13

68

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Proof $G_n$ is an integer

Published on 14 Nov 2019 - 3:52

75

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The number of solutions to the Diophantine-like inequality

Published on 14 Nov 2019 - 23:05

98

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Prove that $\sum_{u = 1}^{N} \sum_{v=1}^{N} \left(\left[\sqrt{u^2-4v} \in Z\right]+\left[\sqrt{u^2+4v} \in Z\right]\right) = D \left(N\right)-1$

Published on 25 Mar 2026 - 23:13

List Question

Analytical solution of $ax+by+cz+dw+... = n$

$3(1^2+2^2+...+n^2)$ is a square

Coincidence in Diophantine solution parametrization for Pythagorean triples etc

Nonlinear polynomial Diophantine equations

Show that $2^n+3^n+5^n+6^n$ isn't a perfect cube, for all $n \in \mathbb{N}$.

When is the number of areas obtained by cutting a circle with $n$ chords a power of $2$?

Conjecture: any two sequences of polygonal numbers will share multiple terms between them

Fermat's Last Theorem for even indices

Does this equation have a solution in the integers: $4^n= \dfrac{x^2+y^2+z^2+w^2}{2}$?

Quartic equation $x^4-y^4=2$ over rationals

If $3\omega^2-2n\omega\psi+\psi^2+1=0$ has a rational solution then it has an integer solution?

Solve quadratic equation with condition that solution should be integer.

Proof $G_n$ is an integer

The number of solutions to the Diophantine-like inequality

Prove that $\sum_{u = 1}^{N} \sum_{v=1}^{N} \left(\left[\sqrt{u^2-4v} \in Z\right]+\left[\sqrt{u^2+4v} \in Z\right]\right) = D \left(N\right)-1$

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