List questions from diophantine-equations

Published on 09 Apr 2018 - 17:42

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Smallest $x+y$ for integer equation $n = 5x + 3y$ in closed form

Published on 12 Apr 2018 - 20:37

200

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When is there a solution to the generalized Pell's equation?

Published on 20 Mar 2026 - 14:28

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General solution for nonlinear Diophantine equation

Published on 16 Apr 2018 - 13:11

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Proof that $x^4 + 4y^4$ cannot be $z^2$

Published on 17 Apr 2018 - 2:01

201

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Diophantine equation $125(m^2+n^2)=(m+n)^3$

Published on 18 Apr 2018 - 13:10

392

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Prove that the number of answers for $|a_1|+|a_2|+...+|a_k| \le n$ is equal to the number of answers for $|a_1|+|a_2|+...+|a_n| \le k$.

Published on 18 Apr 2018 - 16:26

338

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Find all solutions of the equation $13[x]+25\{x\}=271$

Published on 19 Apr 2018 - 6:14

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Find integers $a$, $b$, $c$, $d$ such that $30a + 42b + 70c + 105d = 11$, or prove that no such integers exist

Published on 19 Apr 2018 - 18:16

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How many solution does $1/a+1/b+1/c+1/d=1$ have?

Published on 21 Apr 2018 - 4:58

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The Proof of Infinitude of Pythagorean Triples $(x,x+1,z)$

Published on 25 Mar 2026 - 14:36

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If $a,b\in\mathbb N_+$ satisfy $\sqrt{ab},\sqrt{\frac{a^2+b^2}2}\in\mathbb N_+$, is it necessarily true that $a=b$?

Published on 21 Apr 2018 - 11:32

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Find $x, y, z \in \mathbb{Z}$ such that :

Published on 22 Mar 2026 - 18:13

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How to show that the Condition is Diophantine

Published on 25 Mar 2026 - 7:43

171

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How many integer pairs $(x,y)$ satisfy $|x|^m+|y|^m=r$

Published on 23 Apr 2018 - 2:17

List Question

Diophantine Equation on squares and cubes

Smallest $x+y$ for integer equation $n = 5x + 3y$ in closed form

When is there a solution to the generalized Pell's equation?

General solution for nonlinear Diophantine equation

Proof that $x^4 + 4y^4$ cannot be $z^2$

Diophantine equation $125(m^2+n^2)=(m+n)^3$

Prove that the number of answers for $|a_1|+|a_2|+...+|a_k| \le n$ is equal to the number of answers for $|a_1|+|a_2|+...+|a_n| \le k$.

Find all solutions of the equation $13[x]+25\{x\}=271$

Find integers $a$, $b$, $c$, $d$ such that $30a + 42b + 70c + 105d = 11$, or prove that no such integers exist

How many solution does $1/a+1/b+1/c+1/d=1$ have?

The Proof of Infinitude of Pythagorean Triples $(x,x+1,z)$

If $a,b\in\mathbb N_+$ satisfy $\sqrt{ab},\sqrt{\frac{a^2+b^2}2}\in\mathbb N_+$, is it necessarily true that $a=b$?

Find $x, y, z \in \mathbb{Z}$ such that :

How to show that the Condition is Diophantine

How many integer pairs $(x,y)$ satisfy $|x|^m+|y|^m=r$

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