List questions from diophantine-equations

Published on 14 Apr 2026 - 22:52

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Bound for the equation $a^2 = b^2 + 4n$

Published on 09 Apr 2026 - 10:32

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Prove the diophantine equation $x^2-7y^2=67$ has no solutions

Published on 15 Apr 2026 - 9:37

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Let $k$ be a postive integer number . Then $2k^2+1$ and $3k^2+1$ cannot both be square numbers.

Published on 16 Apr 2026 - 11:19

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Equivalence between a limit and Pillai's Conjecture

Published on 26 Mar 2026 - 12:45

181

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Conjectures on Twin Euler Bricks

Published on 13 Apr 2026 - 8:29

514

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Solving a multivariate quadratic equation in the integers

Published on 24 Apr 2026 - 5:15

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Finding solutions to $2^x+17=y^2$

Published on 13 Apr 2026 - 19:19

861

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Find short and simple methods to solve $24x^4+1=y^2$

Published on 15 Apr 2026 - 11:22

168

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Number of integral solutions to $4y^{3}=3x^{2}+1$

Published on 16 Apr 2026 - 3:14

98

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Does Diophantine equation $(5x-1)yz=(2088k+2010+x)(z-y)$ has solution for every $k\geq1$?

Published on 13 Apr 2026 - 20:44

881

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Prove that the equation $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b} = 6$ has no solutions in natural numbers

Published on 11 Apr 2026 - 21:30

101

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$x^2+x+100 = k^2$, $(x, k) \in \mathbb{N}^2$

Published on 16 Apr 2026 - 17:44

92

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How to solve an inequality involving the floor function?

Published on 08 Apr 2026 - 16:56

143

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Find all integer solutions of the equation $x^2+15^a=2^b$

Published on 14 Apr 2026 - 2:24

List Question

For what kind of positive integers $m+n+m^2+n^2 \mid m^3+n^3$ holds?

Bound for the equation $a^2 = b^2 + 4n$

Prove the diophantine equation $x^2-7y^2=67$ has no solutions

Let $k$ be a postive integer number . Then $2k^2+1$ and $3k^2+1$ cannot both be square numbers.

Equivalence between a limit and Pillai's Conjecture

Conjectures on Twin Euler Bricks

Solving a multivariate quadratic equation in the integers

Finding solutions to $2^x+17=y^2$

Find short and simple methods to solve $24x^4+1=y^2$

Number of integral solutions to $4y^{3}=3x^{2}+1$

Does Diophantine equation $(5x-1)yz=(2088k+2010+x)(z-y)$ has solution for every $k\geq1$?

Prove that the equation $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b} = 6$ has no solutions in natural numbers

$x^2+x+100 = k^2$, $(x, k) \in \mathbb{N}^2$

How to solve an inequality involving the floor function?

Find all integer solutions of the equation $x^2+15^a=2^b$

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