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I have an interesting equation over the naturals.

$x^5=y^2+4$

How do I solve it?

Student12
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    I'd try factoring over $\Bbb Z[i]$. This is a genus $2$ curve and will have only finitely many rational solutions by Faltings' theorem. – Angina Seng Jan 04 '18 at 10:50

1 Answers1

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The equation has no solution mod $11$.

lhf
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  • $11$ seems to be the only prime that works. See https://math.stackexchange.com/questions/1749467/x5-y2-4-has-no-solution-mod-m. – lhf Jan 04 '18 at 10:59