List questions from diophantine-equations

Published on 11 Jun 2020 - 10:14

85

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Exponent of two integers

Published on 12 Jun 2020 - 7:07

128

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Sum of $5$ dice: Number of solutions diophantine equation

Published on 13 Jun 2020 - 0:23

562

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Finding integer solutions to sum of reciprocals of x and y

Published on 14 Jun 2020 - 7:25

65

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How to solve this using linear diophantine equations?

Published on 25 Mar 2026 - 11:12

105

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Show that, there are no integers $(m, n)$ such that, $m^2 + (m + 1)^2 = n^4 + (n + 1)^4$.

Published on 17 Jun 2020 - 17:13

526

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Find all sequences $x_1,x_2,\dots,x_n$ of distinct positive integers such that $\frac{1}{2}=\frac{1}{x_1^2}+\frac{1}{x_2^2}+\dots+\frac{1}{x_n^2}$

Published on 18 Jun 2020 - 21:44

868

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When The Sum Of Squares Of Two Consecutive Integers Is Again A Perfect Square?

Published on 18 Jun 2020 - 22:46

174

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Find prime pairs satisfying this equation

Published on 21 Jun 2020 - 20:04

118

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$x^4-4=y^2+z^2$ prove that it has no integer solution

Published on 29 Mar 2026 - 20:09

75

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Using quadratic residues and/or reciprocity to prove relative primality?

Published on 25 Mar 2026 - 19:04

68

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Diophantine equation : $6^m+2^n+2=x^2$

Published on 23 Jun 2020 - 6:59

204

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Solvability of the Pell-like equation $x^{2}-dy^{2} = k$

Published on 25 Jun 2020 - 0:39

213

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Is there a quick (hopefully elementary) way to prove that $6b^2c^2 + 3c^2 - 36bc - 4b^4 - 4b^2 + 53=0$ has only one solution?

Published on 25 Mar 2026 - 10:57

174

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Proof that no integers satisfy $x^2+2y^2 = p$

Published on 26 Jun 2020 - 13:26

List Question

Determine all pairs of positive integers $(a,b)$ such that $a^2+b^2+ab$ is a perfect square.

Exponent of two integers

Sum of $5$ dice: Number of solutions diophantine equation

Finding integer solutions to sum of reciprocals of x and y

How to solve this using linear diophantine equations?

Show that, there are no integers $(m, n)$ such that, $m^2 + (m + 1)^2 = n^4 + (n + 1)^4$.

Find all sequences $x_1,x_2,\dots,x_n$ of distinct positive integers such that $\frac{1}{2}=\frac{1}{x_1^2}+\frac{1}{x_2^2}+\dots+\frac{1}{x_n^2}$

When The Sum Of Squares Of Two Consecutive Integers Is Again A Perfect Square?

Find prime pairs satisfying this equation

$x^4-4=y^2+z^2$ prove that it has no integer solution

Using quadratic residues and/or reciprocity to prove relative primality?

Diophantine equation : $6^m+2^n+2=x^2$

Solvability of the Pell-like equation $x^{2}-dy^{2} = k$

Is there a quick (hopefully elementary) way to prove that $6b^2c^2 + 3c^2 - 36bc - 4b^4 - 4b^2 + 53=0$ has only one solution?

Proof that no integers satisfy $x^2+2y^2 = p$

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