List questions from diophantine-equations

Published on 21 Jul 2020 - 22:01

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How to express birational equivalence of Diophantine equation $x^4+y^4=z^2$ and elliptic curve?

Published on 31 Mar 2026 - 17:59

161

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Solve $x^2+3y = u^2$ and $y^2+3x=v^2$ in positive integers.

Published on 22 Jul 2020 - 5:56

47

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For which primes $p$ and positive integers $k$ is the deficiency $D(p^k)$ equal to the arithmetic derivative of $p^k$?

Published on 28 Mar 2026 - 15:21

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Is Hilbert's tenth problem decidable for degree $2$?

Published on 23 Feb 2026 - 8:30

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One number is removed from the set of integers from $1$ to $n.$ The average of the remaining numbers is $163/4.$ Which integer was removed?

Published on 28 Mar 2026 - 22:13

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Prove that $x^2 + 8 = 3^y$ has only one solution: $x=1, y=2,$ where $x,y\in \mathbb{N}$

Published on 25 Jul 2020 - 5:54

121

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Find $a,b,c$ if ${(1+3+5+.....a)}+{(1+3+5+....b)}={(1+3+5+.....c)}$

Published on 27 Mar 2026 - 12:08

70

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Kind of Diophantine Equation

Published on 01 Apr 2026 - 6:08

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Mordell equation with prime-power constant

Published on 31 Mar 2026 - 17:57

120

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Distinguish which second degree diophantique equation has a solution without solving them

Published on 28 Jul 2020 - 23:44

471

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Find all positive integers $n$ for which $1372n^4 - 3 $ is an odd perfect square.

Published on 25 Mar 2026 - 12:54

272

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What is a Diophantine equation, and why should we care about them?

Published on 05 Jul 2016 - 23:49

157

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Bounding solutions of a diophantine equation

Published on 25 Mar 2026 - 23:36

69

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Question on the property of algebraic number

Published on 26 Mar 2026 - 3:00

List Question

The diophantine equation $ m = x^2 + 7y^2 $

How to express birational equivalence of Diophantine equation $x^4+y^4=z^2$ and elliptic curve?

Solve $x^2+3y = u^2$ and $y^2+3x=v^2$ in positive integers.

For which primes $p$ and positive integers $k$ is the deficiency $D(p^k)$ equal to the arithmetic derivative of $p^k$?

Is Hilbert's tenth problem decidable for degree $2$?

One number is removed from the set of integers from $1$ to $n.$ The average of the remaining numbers is $163/4.$ Which integer was removed?

Prove that $x^2 + 8 = 3^y$ has only one solution: $x=1, y=2,$ where $x,y\in \mathbb{N}$

Find $a,b,c$ if ${(1+3+5+.....a)}+{(1+3+5+....b)}={(1+3+5+.....c)}$

Kind of Diophantine Equation

Mordell equation with prime-power constant

Distinguish which second degree diophantique equation has a solution without solving them

Find all positive integers $n$ for which $1372n^4 - 3 $ is an odd perfect square.

What is a Diophantine equation, and why should we care about them?

Bounding solutions of a diophantine equation

Question on the property of algebraic number

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