An elliptic Diophantine equation from the study of partitions

Abstract

We present the elliptic equation X3 + 2 = Y 2 as the rst in
a sequence of Diophantine equations arising from some new results in
the theory of partitions of multisets with equal sums. Two proofs for
Theorem 2.3, showing that the only integer solutions to this equation
are (-1; 1) and (-1;