How many positive integers z are there such that x(x + z) = y^{2} has no solutions in positive integers x, y? Crux Mathematicorum, Sept. 2006, p. 288, Colombian Math Olympiad. © Copyright 2007 Stan Wagon. Reproduced with permission.

How many positive integers z are there such that x(x + z) = y^{2} has no solutions in positive integers x, y?

Crux Mathematicorum, Sept. 2006, p. 288, Colombian Math Olympiad.

© Copyright 2007 Stan Wagon. Reproduced with permission.