6

Part of 2017 German National Olympiad

Problems(1)

Consecutive perfect squares adding up to a perfect cube

Source: Germany 2017, Problem 6

Prove that there exist infinitely many positive integers

m

such that there exist

m

consecutive perfect squares with sum

m^3

. Specify one solution with

m>1

number theorynumber theory proposedGermanyDiophantine equationDiophantine Equations