# Questions tagged [diophantine-equations]

Use for questions about finding integer or rational solutions to polynomial equations.

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### Conditions for solutions $a^3 - b^3 = n$

While investigating $a^n - b^n$, I obtained conditions on $n$ for $a^2 - b^2 = n$. However, starting from the 3rd power, the problem becomes significantly more complex. Although something can still be ...
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### Are there solutions of $a^n+n+b^n=c^n$ for $n>2$?

This question has been extensively edited to meet site requirements. As is well-known, the Diophantine equation $a^n+b^n=c^n$ has many solutions when $n=2$ (Pythagorean triples) but none when $n>2$ ...
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### solving a Diophantine equation $17+2^m=n^2$ [duplicate]

What is the method to solve $$17+2^m=n^2$$ for positive integers $m$ and $n$. I tried using modular arithmetic which seems did not help.
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### How do I solve this Diophantine equation?

How do I solve this Diophantine equation, $a^{2n}+b^2=c^{2n}$, where $n$ is any postive integer $>1$ & $a,b,c\ne0$? I tried it by applying the Pythagorean triplets generating formula, but ...
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