Sum of consecutive squares or cubes is a square or cube
Source: Moldova 2007 IMO-BMO TST II problem 1
March 23, 2007
geometry3D geometryalgebrafactorizationsum of cubesnumber theory proposednumber theory
Problem Statement
Find the least positive integers such that
a) There exist consecutive natural numbers whose sum of cubes is also a cube.
b) There exist consecutive natural numbers whose sum of squares is also a square.
The author is Vasile Suceveanu