List questions from diophantine-equations

Published on 11 Dec 2014 - 23:38

47

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How do I prove that $x^s=(-1)^k \sum_{k=0}^{(r-1)/2}\binom{r}{2k}p^{s(r-2k)}$ has no solutions?

Published on 12 Dec 2014 - 22:52

710

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How to solve $y^2=3x^4+3x^2+1$ for integers.

Published on 14 Dec 2014 - 20:38

521

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Find the integral solutions to $ x^2+y^2+z^2=x^2y^2$

Published on 15 Dec 2014 - 17:36

621

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Simple Question On Relationship Between Cubes And Squares

Published on 29 Mar 2026 - 4:48

157

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Is there a solution to $a^4+(a+d)^4+(a+2d)^4+(a+3d)^4+\dots = z^4$?

Published on 17 Dec 2014 - 18:37

316

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Congruence properties of $a^5+b^5+c^5+d^5+e^5=0$?

Published on 18 Dec 2014 - 2:44

429

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When can $n^k+k$ be a perfect square?

Published on 18 Dec 2014 - 15:04

105

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Neat Diophantine Equation Question

Published on 18 Dec 2014 - 16:21

331

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Diophantine equation involving factorial ...

Published on 18 Dec 2014 - 16:31

283

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Solve $y^2=x^3-4$ in $x,y\in \mathbb{Z}$

Published on 24 Mar 2026 - 22:09

87

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

Published on 18 Dec 2014 - 21:03

55

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How to solve the diophantine equation $n^3-n-1=k^2-k+1$?

Published on 18 Dec 2014 - 21:35

87

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Solve $y^2=x^4+x+2$ in $x,y\in \mathbb{Z}$

Published on 18 Dec 2014 - 22:16

291

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Find all integers that make this expression rational

Published on 19 Dec 2014 - 0:49

List Question

Diophantin equation $a^3+b^3=c^3+5$

How do I prove that $x^s=(-1)^k \sum_{k=0}^{(r-1)/2}\binom{r}{2k}p^{s(r-2k)}$ has no solutions?

How to solve $y^2=3x^4+3x^2+1$ for integers.

Find the integral solutions to $ x^2+y^2+z^2=x^2y^2$

Simple Question On Relationship Between Cubes And Squares

Is there a solution to $a^4+(a+d)^4+(a+2d)^4+(a+3d)^4+\dots = z^4$?

Congruence properties of $a^5+b^5+c^5+d^5+e^5=0$?

When can $n^k+k$ be a perfect square?

Neat Diophantine Equation Question

Diophantine equation involving factorial ...

Solve $y^2=x^3-4$ in $x,y\in \mathbb{Z}$

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

How to solve the diophantine equation $n^3-n-1=k^2-k+1$?

Solve $y^2=x^4+x+2$ in $x,y\in \mathbb{Z}$

Find all integers that make this expression rational

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