Noam Elkies

Diophantine equations, one of the oldest topics of mathematical research, remain the object of intense and fruitful study. A rational solution to a system of algebraic equations is tantamount to a point with rational coordinates (briefly, a "rational...

By a "rational triangle" we mean a plane triangle whose sides are rational numbers. By Heron's formula, there exists such a triangle of area sqrt(a) if and only if a > 0 and x y z (x + y + z) = a for some rationals x, y, z. In a 1749 letter to...

Abstract: Diophantine equations, one of the oldest topics of mathematical research, remain the object of intense and fruitful study. A rational solution to a system of algebraic equations is tantamount to a point with rational coordinates (briefly, a...