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

Abstract

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.

References in corpus (4)

• On the Diophantine equation $(x+1{)}^k+(x+2{)}^k+...+(2x{)}^k=y^n$
• On perfect powers that are sums of cubes of a three term arithmetic progression
• Perfect powers that are sums of consecutive squares
• On the Diophantine equation $(x+1{)}^k+(x+2{)}^k+...+(lx{)}^k=y^n$