The following problem was proposed by A. Schinzel a couple of days ago at the 22nd Conference on Number Theory, held in Liptovsky Jan (Slovakia). He pointed out that the question has an affirmative answer in the case $x \le 3$, but nothing else in the remaining cases:
Question: Let $x$ and $y$ be integers greater than $3$ for which, whenever $n$ is a positive integer, it holds $$ 1+2^x+\ldots+n^x \,\,\mathrm{ divides }\,\, 1+2^y+\ldots+n^y. $$ Does it follow that $x=y$?