On the sum of consecutive cubes being a perfect square

Abstract

In this paper estimates of linear forms in elliptic logarithms are applied to solve the problem of determining, for given n 2, all sets of n consecutive cubes adding up to a perfect square. Use is made of a lower bound of linear forms in elliptic logarithms recently obtained by Sinnou David. Complete sets of solutions are provided for all n between 2 and 50, and for n = 98.