KöMaL problem A, 2014

Number theory Difficulty 4.0 AIME Prove it Hungary

Prove that the equation $x^3 - x + 9 = 5 y^2$ has no solution among the integers.
(5 pont)

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: KöMaL, licensed Rights held by KöMaL and the MATFUND Foundation. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.