Mathematicians Crack a Simple but Stubborn Class of Equations

In the third century BCE, Archimedes posed a riddle about herding cattle that, he claimed, only a truly wise person could solve. His problem ultimately boiled down to an equation that involves the difference between two squared terms, which can be written as x2 – dy2 = 1. Here, d is an integer — a positive or negative counting number — and Archimedes was looking for solutions where both x and y…

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