List questions from diophantine-equations

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Necessary and sufficient conditions that the difference of two quadratic equations has no solutions in $\mathbb{N}$

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The quadratic diophantine $ k^2 - 1 = 5(m^2 - 1)$

Published on 16 Apr 2026 - 7:32

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How to solve $5^{2x}-3\cdot2^{2y}+5^x\cdot2^{y-1}-2^{y-1}-2\cdot5^x+1=0$ in $\mathbb{Z}$

Published on 17 Apr 2026 - 6:47

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Generate solutions of Quadratic Diophantine Equation

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Solutions to $\binom{n}{5} = 2 \binom{m}{5}$

Published on 15 Apr 2026 - 0:39

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Solving the algebraic equation

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Minimum of $n$? $123456789x^2 - 987654321y^2 =n$ ($x$,$y$ and $n$ are positive integers)

Published on 15 Apr 2026 - 3:47

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Sum of three cubes $x^3+y^3+z^3=2$ and parametric solutions

Published on 16 Apr 2026 - 14:23

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Proving there are no integers $a, b, c$ satisfying $12a + 18b + 27c = 227$

Published on 14 Apr 2026 - 23:45

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Foundation on Diophantine Analysis and Number Theory

Published on 11 Apr 2026 - 4:37

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A Rational Parameterization of Multiple Simple Expressions (Or the intersection of two rational parameterizations)

Published on 14 Apr 2026 - 23:57

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List all the pairs $(x,y)$ s.t. $x^2 - y^2 = 2020$

Published on 17 Apr 2026 - 13:31

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Multi variable Diophantine equation

Published on 12 Apr 2026 - 4:12

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Does the equation $\sigma(\sigma(x^2))=2x\sigma(x)$ have any odd solutions?

Published on 12 Apr 2026 - 8:31

List Question

$x^4-4y^4=z^2$ has no solution in positive integers $x$, $y$, $z$.

Necessary and sufficient conditions that the difference of two quadratic equations has no solutions in $\mathbb{N}$

The quadratic diophantine $ k^2 - 1 = 5(m^2 - 1)$

How to solve $5^{2x}-3\cdot2^{2y}+5^x\cdot2^{y-1}-2^{y-1}-2\cdot5^x+1=0$ in $\mathbb{Z}$

Generate solutions of Quadratic Diophantine Equation

Solutions to $\binom{n}{5} = 2 \binom{m}{5}$

Solving the algebraic equation

Minimum of $n$? $123456789x^2 - 987654321y^2 =n$ ($x$,$y$ and $n$ are positive integers)

Sum of three cubes $x^3+y^3+z^3=2$ and parametric solutions

Proving there are no integers $a, b, c$ satisfying $12a + 18b + 27c = 227$

Foundation on Diophantine Analysis and Number Theory

A Rational Parameterization of Multiple Simple Expressions (Or the intersection of two rational parameterizations)

List all the pairs $(x,y)$ s.t. $x^2 - y^2 = 2020$

Multi variable Diophantine equation

Does the equation $\sigma(\sigma(x^2))=2x\sigma(x)$ have any odd solutions?

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