On perfect powers that are sums of cubes of a five term arithmetic progression

Alejandro Argáez-García

We prove that the equation $(x-2r{)}^3+(x-r{)}^3+x^3+(x+r{)}^3+(x+2r{)}^3=y^p$ only has solutions which satisfy $xy=0$ for $1\le r\le 10^6$ and $p\ge 5$ prime.