List questions from diophantine-equations

Published on 25 Aug 2015 - 8:35

158

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Solutions to a quadratic diophantine modular equation

Published on 07 Apr 2026 - 20:31

162

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Solving a system of two equations

Published on 25 Aug 2015 - 18:37

385

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Diophantine equation: $13^x+3=y^2$

Published on 29 Mar 2026 - 11:01

367

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Pentagonal Numbers

Published on 26 Aug 2015 - 15:42

523

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Prove that for any integers $x,y,z$ there exist $a,b,c$ such that $ax+by+cz=0$

Published on 27 Aug 2015 - 0:36

439

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Can the determinant of an integer matrix with a given row be any multiple of the gcd of that row?

Published on 03 Apr 2026 - 4:19

140

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Difficult sets of Equations, counting

Published on 27 Aug 2015 - 17:10

122

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Thue equation $ x^4 - 6 x^3 y - x^2 y^2 + 6 x y^3 - y^4=-1 $

Published on 27 Aug 2015 - 22:56

105

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If $(a+b)^n=\sum_{k=0}^{n}{n\choose k}a^{n-k}b^kc_k$, then $c_k=1$?

Published on 28 Aug 2015 - 0:05

100

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Is there an integer solution to $x^2+1978=y^2$

Published on 28 Aug 2015 - 9:42

635

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Can the determinant of an integer matrix with $k$ given rows equal the gcd of the $k\times k$ minors of those rows?

Published on 29 Mar 2026 - 13:40

52

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Does there exist a finite set of homogeneous polynomials (+ property) whose unique solution is equivalent to a finite sequence of naturals?

Published on 29 Aug 2015 - 4:04

419

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Find all integers $m,n$ for which $m^2+n^2$ is a square and $\sqrt{\frac{2m^2+2}{n^2+1}}$ is rational

Published on 29 Aug 2015 - 23:43

1.6k

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Can 720! be written as the difference of two positive integer powers of 3?

Published on 03 Apr 2026 - 16:15

List Question

How can I solve $x^2+2=y^3$ in $\mathbb{Z}$?

Solutions to a quadratic diophantine modular equation

Solving a system of two equations

Diophantine equation: $13^x+3=y^2$

Pentagonal Numbers

Prove that for any integers $x,y,z$ there exist $a,b,c$ such that $ax+by+cz=0$

Can the determinant of an integer matrix with a given row be any multiple of the gcd of that row?

Difficult sets of Equations, counting

Thue equation $ x^4 - 6 x^3 y - x^2 y^2 + 6 x y^3 - y^4=-1 $

If $(a+b)^n=\sum_{k=0}^{n}{n\choose k}a^{n-k}b^kc_k$, then $c_k=1$?

Is there an integer solution to $x^2+1978=y^2$

Can the determinant of an integer matrix with $k$ given rows equal the gcd of the $k\times k$ minors of those rows?

Does there exist a finite set of homogeneous polynomials (+ property) whose unique solution is equivalent to a finite sequence of naturals?

Find all integers $m,n$ for which $m^2+n^2$ is a square and $\sqrt{\frac{2m^2+2}{n^2+1}}$ is rational

Can 720! be written as the difference of two positive integer powers of 3?

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