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Diophantus studied algebraic problems seeking numerical solutions, preserved in the Arithmetica. Many of those problems ask for positive rational numbers; their scope therefore differs from the exclusively integer formulation often associated with modern Diophantine equations.^[ref]

Book II, Problem 8 asks for a square to be split into two squares. In modern notation, $16=(12/5{)}^2+(16/5{)}^2$ gives a concrete rational example. The problem connects algebraic manipulation with the search for rational points on a curve, through exact algebraic relations.^[ref]