n^p $ has $ 1009^{2018} $ natural (x, y) solutions. n is natural number, p is a prime and $ p<10000 $. Find values of p.

Asked Jan 08 '22 at 19:06

Active Jan 08 '22 at 19:06

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I have a few observations: if y = a, x = b is a solution then y = b, x = a is also a solution. $1009^{2018}$ is uneven so x = y is a solution. Could you give me some hints how to continue solving this problem?

asked Jan 08 '22 at 19:06

prapola

1

See here for a solution method. – Dietrich Burde Jan 08 '22 at 19:11
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The problem is outdated. It is already $2022$. – markvs Jan 08 '22 at 19:16
Thanks, I solved it. – prapola Jan 08 '22 at 19:47

Equation $ 1/x + 1/y = 1/n^p $ has $ 1009^{2018} $ natural (x, y) solutions. n is natural number, p is a prime and $ p<10000 $. Find values of p.

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