List questions from diophantine-equations

Published on 16 Sep 2023 - 15:12

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On sixth powers $a^6+b^{12}+c^{12} = d^6+e^{12}+f^{12}$?

Published on 29 Mar 2026 - 21:58

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General parametric solution of Diophantine Equation--4th Powers

Published on 01 Apr 2026 - 11:57

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Sums of three cubes of form $a^3+b^3+c^3=(c+1)^3$?

Published on 27 Sep 2023 - 7:41

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If $x>y\ge1$ are integers, with $x$ even and $y$ odd, and $x^4+4x^3y-4xy^3-4y^4$ is a square, must $y \mid x$?

Published on 30 Mar 2026 - 20:55

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Solutions of $x^n-1=a^m$

Published on 01 Oct 2023 - 18:52

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Finding rational points on the elliptic curve for $A^4+B^4 = C^4+D^4$?

Published on 02 Apr 2026 - 12:36

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Number of Ordered Factorisations

Published on 07 Oct 2023 - 9:36

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Solve the Diophantine equation $m!n! = m!+n!$.

Published on 02 Apr 2026 - 5:05

130

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Find all integer quadruples $(a,b,x,y)$ satisfying $a^x-b^y=(ab)^{x-y}$

Published on 05 Apr 2026 - 22:06

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Skolem’s “Theorem 9” and the associated equation

Published on 23 Feb 2026 - 8:31

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Solutions to a system of diophantine equations

Published on 11 Oct 2023 - 21:35

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Prove that this equality is not achieved : $21+a^{2}+a^{bc}≠ a^{c+1}+a^{c+1}+(bc)^{a}$

Published on 14 Oct 2023 - 19:56

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When is $\mathbb{F}_{p^k}^{\times} \cong \mathbb{Z}_m^{\times}$ for $k>1$?

Published on 21 Oct 2023 - 2:35

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Are there any general results that relate the amount of solutions to a diophantine equations to the average growth rate of such solutions?

Published on 28 Mar 2026 - 8:50

List Question

Diophantine equation, how many solutions such that $x \ge 0$ and $y \ge 0$.

On sixth powers $a^6+b^{12}+c^{12} = d^6+e^{12}+f^{12}$?

General parametric solution of Diophantine Equation--4th Powers

Sums of three cubes of form $a^3+b^3+c^3=(c+1)^3$?

If $x>y\ge1$ are integers, with $x$ even and $y$ odd, and $x^4+4x^3y-4xy^3-4y^4$ is a square, must $y \mid x$?

Solutions of $x^n-1=a^m$

Finding rational points on the elliptic curve for $A^4+B^4 = C^4+D^4$?

Number of Ordered Factorisations

Solve the Diophantine equation $m!n! = m!+n!$.

Find all integer quadruples $(a,b,x,y)$ satisfying $a^x-b^y=(ab)^{x-y}$

Skolem’s “Theorem 9” and the associated equation

Solutions to a system of diophantine equations

Prove that this equality is not achieved : $21+a^{2}+a^{bc}≠ a^{c+1}+a^{c+1}+(bc)^{a}$

When is $\mathbb{F}_{p^k}^{\times} \cong \mathbb{Z}_m^{\times}$ for $k>1$?

Are there any general results that relate the amount of solutions to a diophantine equations to the average growth rate of such solutions?

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