# A Pythagoras-style Diophantine Equation and its Solution

The Pythagorean equation x^2 + y^2 = z^2 (to be solved over the positive integers N) is a much-studied one; many articles have appeared in this magazine alone, devoted to this equation. A close relative to this is the equation 1/x + 1/y = 1/z (which can be written as x^−1 + y^−1 = z^−1 ; in this form, its similarity to the Pythagorean equation is readily seen), and this too has been studied many times in At Right Angles.

In this note, we study another equation which visually resembles the Pythagorean equation and which too is required to be solved over the positive integers:

1/√x + 1/√y = 1/√z