List questions from diophantine-equations

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Is there a general formula for three Pythagorean Triangles which share an area?

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Prove that there are no integers $x$ and $y$ such that $3x^2=13+4y^2$

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Level lowering the generalized Fermat equation

Published on 17 Apr 2026 - 13:29

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Diophantine equation and regular polygons

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Find all the integer solutions of $x^2-y^2=a^2+mb^2$

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Integer Solutions of $x^4+y^4=z^2$

Published on 16 Apr 2026 - 2:40

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When does the Diophantine equation $ax + by + cz = d$ have a solution?

Published on 11 Apr 2026 - 17:44

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How to solve the Diophantine equation：$x^2+xy+y^2=r^2,x,y,r\in \Bbb Z$

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When can we solve a diophantine equation with degree $2$ in $3$ unknowns completely?

Published on 12 Apr 2026 - 13:20

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Is there a formula for this specific pattern of Pythagorean Triangles sharing an area?

Published on 15 Apr 2026 - 19:07

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Equation with solution in prime numbers

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Prove that the largest prime $< z$ does not divide $x$

Published on 10 Apr 2026 - 22:41

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Set of non-zero elements in ring of integers $\mathcal{O}_K$ in a number field $K$ is diophantine.

Published on 16 Apr 2026 - 1:46

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How to find $x$ such that $a^2-b^2-(c+d)x=r^2$; $c^2-d^2+(a+b)x=s^2$

Published on 17 Apr 2026 - 1:50

List Question

Solving diophantine equations of 4-5 variables

Is there a general formula for three Pythagorean Triangles which share an area?

Prove that there are no integers $x$ and $y$ such that $3x^2=13+4y^2$

Level lowering the generalized Fermat equation

Diophantine equation and regular polygons

Find all the integer solutions of $x^2-y^2=a^2+mb^2$

Integer Solutions of $x^4+y^4=z^2$

When does the Diophantine equation $ax + by + cz = d$ have a solution?

How to solve the Diophantine equation：$x^2+xy+y^2=r^2,x,y,r\in \Bbb Z$

When can we solve a diophantine equation with degree $2$ in $3$ unknowns completely?

Is there a formula for this specific pattern of Pythagorean Triangles sharing an area?

Equation with solution in prime numbers

Prove that the largest prime $< z$ does not divide $x$

Set of non-zero elements in ring of integers $\mathcal{O}_K$ in a number field $K$ is diophantine.

How to find $x$ such that $a^2-b^2-(c+d)x=r^2$; $c^2-d^2+(a+b)x=s^2$

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