List questions from diophantine-equations

Published on 11 Apr 2026 - 3:30

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How to find a three digit number which,when reversed, becomes equal to $17$ times the square of it's cube root?

Published on 14 Apr 2026 - 11:36

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Linear diophantine equation $100x - 23y = -19$

Published on 28 Mar 2026 - 5:30

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Determine if equation will generate perfect squares

Published on 09 Apr 2026 - 22:04

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All positive integer solutions to $\frac{1}{x_1}+\frac{1}{x_2}+\cdots+\frac{1}{x_n}+\frac{1}{x_1 x_2 \cdots x_n}=1$

Published on 17 Apr 2026 - 10:05

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What is the simplest ellipse that goes through exactly 13 lattice points?

Published on 11 Apr 2026 - 17:41

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For which $n$ are there primitive Pythagorean triples with legs of lengths $a$ and $a+n$?

Published on 15 Apr 2026 - 6:38

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How to prove $\sqrt3$ is irrational?

Published on 11 Apr 2026 - 1:03

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How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?

Published on 15 Apr 2026 - 15:24

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$XX^t=A$, $X=?$. Where $X \in \{0,1\}^{n \times m}$

Published on 17 Apr 2026 - 12:45

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Given $XX^\top=A$, solving for $X$

Published on 14 Apr 2026 - 16:30

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The sum of the first $n$ squares is a square: a system of two Pell-type-equations

Published on 13 Apr 2026 - 13:00

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Can $x^{n}-1$ be prime if $x$ is not a power of $2$ and $n$ is odd?

Published on 23 Apr 2026 - 10:46

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Do the solutions to the unit equation lie dense in the complex numbers

Published on 10 Apr 2026 - 17:38

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Integral solutions of $x^2+y^2+1=z^2$

Published on 15 Apr 2026 - 22:37

List Question

Number of solutions of Frobenius equation

How to find a three digit number which,when reversed, becomes equal to $17$ times the square of it's cube root?

Linear diophantine equation $100x - 23y = -19$

Determine if equation will generate perfect squares

All positive integer solutions to $\frac{1}{x_1}+\frac{1}{x_2}+\cdots+\frac{1}{x_n}+\frac{1}{x_1 x_2 \cdots x_n}=1$

What is the simplest ellipse that goes through exactly 13 lattice points?

For which $n$ are there primitive Pythagorean triples with legs of lengths $a$ and $a+n$?

How to prove $\sqrt3$ is irrational?

How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?

$XX^t=A$, $X=?$. Where $X \in \{0,1\}^{n \times m}$

Given $XX^\top=A$, solving for $X$

The sum of the first $n$ squares is a square: a system of two Pell-type-equations

Can $x^{n}-1$ be prime if $x$ is not a power of $2$ and $n$ is odd?

Do the solutions to the unit equation lie dense in the complex numbers

Integral solutions of $x^2+y^2+1=z^2$

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