Problem of the Week 978

A Diophantine Problem

Find all solutions in nonnegative integers to x^4 + (x+1)^4 = y^2 + (y+1)^2.

Source: Source: A problem book designed for Olympiad practice by Edward Lozansky and Cecil Rousseau: Winning Solutions, Springer 1996. This one is from an old Hungarian competition.
© Copyright 2003 Stan Wagon. Reproduced with permission.

19 February 2003