List questions from diophantine-equations

125

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Show that for any positive integer $n>1$ there exist positive integers $x$ and $y$ such that $n^3+x^3=(x-1)^3+y^3$.

Published on 01 Jun 2020 - 21:01

28

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Value of m for which the function will give integers as an output.

Published on 02 Jun 2020 - 10:49

1.6k

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Find all integer solutions for $x^3+1=y^2$.

Published on 02 Jun 2020 - 22:46

945

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All integer solutions of $x^3-y^3=2020$.

Published on 03 Jun 2020 - 14:19

953

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Solve $x^2-2^y=2021$ for $x,y\in\mathbb{N}$

Published on 03 Jun 2020 - 18:15

59

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How to solve this algebra problem related to Pythagorean triplets?

Published on 26 Mar 2026 - 17:36

101

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Solve in $\mathbb Z$ the equation $(x+y)(x^2+y^2)=4xy+3$

Published on 04 Jun 2020 - 18:32

87

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find all pairs of natural numbers $(x, y)$ so that $121$ divides $x^2+y^2$

Published on 04 Jun 2020 - 19:53

89

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Solve $(x+1)^2y + (y+1)^2x=0, x, y \in \mathbb{Z} $

Published on 06 Jun 2020 - 7:04

137

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polynomial equation $ A(x+y_1)(x+y_2)...(x+y_n) + B(x+z_1)(x+z_2)...(x+z_k) = f(x) $ ??

Published on 07 Jun 2020 - 22:29

73

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Positive solutions to this exponential diophantine

Published on 08 Jun 2020 - 12:42

179

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Proof of "equations cannot have an integral solutions" using modular arithmetic.

Published on 09 Jun 2020 - 12:02

164

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$x^2 + 2y^2=3^k$

Published on 09 Jun 2020 - 12:40

152

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Solving second-degree diophantine equation

Published on 09 Jun 2020 - 17:06

740

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Solve the following equation in integers $x,y:$ $x^2+6xy+8y^2+3x+6y=2.$

Published on 09 Jun 2020 - 20:22

List Question

Show that for any positive integer $n>1$ there exist positive integers $x$ and $y$ such that $n^3+x^3=(x-1)^3+y^3$.

Value of m for which the function will give integers as an output.

Find all integer solutions for $x^3+1=y^2$.

All integer solutions of $x^3-y^3=2020$.

Solve $x^2-2^y=2021$ for $x,y\in\mathbb{N}$

How to solve this algebra problem related to Pythagorean triplets?

Solve in $\mathbb Z$ the equation $(x+y)(x^2+y^2)=4xy+3$

find all pairs of natural numbers $(x, y)$ so that $121$ divides $x^2+y^2$

Solve $(x+1)^2y + (y+1)^2x=0, x, y \in \mathbb{Z} $

polynomial equation $ A(x+y_1)(x+y_2)...(x+y_n) + B(x+z_1)(x+z_2)...(x+z_k) = f(x) $ ??

Positive solutions to this exponential diophantine

Proof of "equations cannot have an integral solutions" using modular arithmetic.

$x^2 + 2y^2=3^k$

Solving second-degree diophantine equation

Solve the following equation in integers $x,y:$ $x^2+6xy+8y^2+3x+6y=2.$

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