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Problem of the Week 1087

A Double Diophantine Dot Product

What is the smallest n having the form n = a b + c d = e f + g h where a, b, c, d, e, f, g, h are distinct positive integers?

Source: Belarus Math Olympiad, 2002. Crux Mathematicorum Nov 2007, p. 421.

© Copyright 2007 Stan Wagon. Reproduced with permission.

26 November 2007