List questions from diophantine-equations

Published on 23 Jun 2015 - 14:55

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Solve in positive integers: $5^x 7^y +4=3^z$

Published on 23 Jun 2015 - 23:03

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Generalizing the Pell equation $x^2-61y^2 = 1$

Published on 24 Jun 2015 - 7:45

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Maximize the following sum

Published on 25 Mar 2026 - 19:01

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How many non-negative integer solutions does $x_1+x_2+\cdots+x_n=A$ have?

Published on 25 Mar 2026 - 20:34

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for which values of $\theta$.does this equation: $x_1^{\sin\theta}+\cdots+x_n^{\sin\theta}=1$ have rational solutions for all $n$?

Published on 04 Apr 2026 - 17:49

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Write $x(a^2+b^2)+(2ab)y$ as a product of factors.

Published on 27 Jun 2015 - 1:20

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Square numbers in the form $1+4y$

Published on 31 Mar 2026 - 22:49

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Solve $n(n+1)(n+2)=6m^3$ in positive integers

Published on 01 Jul 2015 - 12:37

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To find positive integers $n$ such that $\dfrac {n(n+1)(n+2)}6$ is a perfect square

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Substitutions that transform Fermat Equations to Elliptic Curves

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Solve $x^n+z^n=(x+1)^n$ for $n\ge 3$ without FLT

Published on 02 Jul 2015 - 11:48

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Can the solvability of a single Diophantine equation be undecidable (in any sense of the word)?

Published on 02 Jul 2015 - 18:37

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Are all even numbers the difference of prime powers

Published on 26 Mar 2026 - 6:21

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Showing there is no triplet of positive integers $(a,b,c)$ satisfying $a^7+b^7=7^c$

Published on 04 Jul 2015 - 1:27

List Question

Finding integers of the form $m+n$ that satisfies $m+n+mn=118$

Solve in positive integers: $5^x 7^y +4=3^z$

Generalizing the Pell equation $x^2-61y^2 = 1$

Maximize the following sum

How many non-negative integer solutions does $x_1+x_2+\cdots+x_n=A$ have?

for which values of $\theta$.does this equation: $x_1^{\sin\theta}+\cdots+x_n^{\sin\theta}=1$ have rational solutions for all $n$?

Write $x(a^2+b^2)+(2ab)y$ as a product of factors.

Square numbers in the form $1+4y$

Solve $n(n+1)(n+2)=6m^3$ in positive integers

To find positive integers $n$ such that $\dfrac {n(n+1)(n+2)}6$ is a perfect square

Substitutions that transform Fermat Equations to Elliptic Curves

Solve $x^n+z^n=(x+1)^n$ for $n\ge 3$ without FLT

Can the solvability of a single Diophantine equation be undecidable (in any sense of the word)?

Are all even numbers the difference of prime powers

Showing there is no triplet of positive integers $(a,b,c)$ satisfying $a^7+b^7=7^c$

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