Diophantine equation

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 discuss the conditions that must be satisfied by the sides of an arbitrary integer-sided triangle if its medians can serve as the sides of a right-angled triangle.
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