KöMaL problem A, 2017

Algebra Difficulty 6.0 National Olympiad Find the answer Hungary

Let $k\ge2$ be an integer. Determine all those polynomials $p(x)$ with real coefficients for which

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.