Problem of the Week 1094

Relatively Prime Integers

Let a, b and c be integers with no factor in common to all three such that 1/a + 1/b = 1/c.

Prove that (a + b), (a - c) and (b - c) are all perfect squares.

Source: School Science and Mathematics 63, October 1963, p. 604.

© Copyright 2008 Andrew Beveridge and Stan Wagon. Reproduced with permission.