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 $1\leq r\leq 10^6$ and $p\geq 5$ prime.
On perfect powers that are sums of cubes of a nine term arithmetic progression
On perfect powers that are sums of cubes of a three term arithmetic progression
Perfect powers that are sums of squares in a three term arithmetic progression
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