List questions from diophantine-equations

Published on 28 Nov 2018 - 21:40

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Does this polynomial have a rational value which is the square of a rational number?

Published on 25 Mar 2026 - 21:48

103

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Use of diophantine equation (money problems, 3 variables)

Published on 25 Mar 2026 - 6:10

147

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find all $k$ such that $k^5+3$ is divisible by $k^2+1$

Published on 29 Nov 2018 - 15:40

55

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given $p,q,r \ge 3$ study the diophantine equation $x^py^q=z^r-1$ using the $abc$-conjecture

Published on 19 Mar 2026 - 20:38

320

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Solving the Diophantine equation $y^2 = 4x^3 + 1$ for $x,y \in \mathbb{Z}$

Published on 30 Nov 2018 - 20:31

392

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Solving the homogeneous Diophantine equation $x^3 + 2y^3 = 7z^3$ for $x,y,z \in \mathbb{Q}$

Published on 20 Mar 2026 - 0:23

273

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Rational solution to a system of equations

Published on 25 Mar 2026 - 21:47

176

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Find all non-negative integers $a, b$ satisfying $|4a^2 - b^{b+1}| \leq 3$

Published on 01 Dec 2018 - 23:18

75

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Conditions on those Pell-type equations to admit solutions

Published on 03 Dec 2018 - 9:00

266

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Quick! Prove that $3^{15}+37$ is a square.

Published on 25 Mar 2026 - 6:08

98

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Problem parallel to Goldbach Conjecture

Published on 07 Dec 2018 - 15:32

102

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Solving the Diophantine equation $y^2 = x^4+x+ 2$ for $x,y \in \mathbb{Z}$

Published on 07 Dec 2018 - 19:39

134

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Showing that the Diophantine equation $3x^2 + 6y^6 + 1 = 8xy^3$ has no solutions $x,y \in \mathbb{Q}$

Published on 07 Dec 2018 - 20:30

263

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Solving the Diophantine equation $y^3 = 4x^2+4x+ 5$ for $x,y \in \mathbb{Z}$

Published on 25 Mar 2026 - 6:05

List Question

Derivation of the Frey curve for $a^2+b^6=c^p$

Does this polynomial have a rational value which is the square of a rational number?

Use of diophantine equation (money problems, 3 variables)

find all $k$ such that $k^5+3$ is divisible by $k^2+1$

given $p,q,r \ge 3$ study the diophantine equation $x^py^q=z^r-1$ using the $abc$-conjecture

Solving the Diophantine equation $y^2 = 4x^3 + 1$ for $x,y \in \mathbb{Z}$

Solving the homogeneous Diophantine equation $x^3 + 2y^3 = 7z^3$ for $x,y,z \in \mathbb{Q}$

Rational solution to a system of equations

Find all non-negative integers $a, b$ satisfying $|4a^2 - b^{b+1}| \leq 3$

Conditions on those Pell-type equations to admit solutions

Quick! Prove that $3^{15}+37$ is a square.

Problem parallel to Goldbach Conjecture

Solving the Diophantine equation $y^2 = x^4+x+ 2$ for $x,y \in \mathbb{Z}$

Showing that the Diophantine equation $3x^2 + 6y^6 + 1 = 8xy^3$ has no solutions $x,y \in \mathbb{Q}$

Solving the Diophantine equation $y^3 = 4x^2+4x+ 5$ for $x,y \in \mathbb{Z}$

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