Problem A. 659. (January 2016)

A. 659. For which \(\displaystyle n\) are there polynomials \(\displaystyle g(x)\) and \(\displaystyle h(x)\) with real coefficients and degrees smaller than \(\displaystyle n\) such that \(\displaystyle g\big(h(x)\big)= x^n+x^{n-1}+x^{n-2}+\dots +x^2+x+1\)?

Miklós Schweitzer Competition, 2015

(5 pont)

Deadline expired on February 10, 2016.

Statistics:

6 students sent a solution.
5 points:	Glasznova Maja, Imolay András, Williams Kada.
3 points:	2 students.
0 point:	1 student.

Problems in Mathematics of KöMaL, January 2016