For more material on this topic, see subtopic Diophantine Equations. To expand search, see Algebra. Laterally related topics: Solutions of Polynomial Equations, Solutions of Linear Equations, Group Theory, and Imaginary and Complex Numbers.
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Swift, J. D. Diophantus of Alexandria. American Mathematical Monthly 63 (1956), 163--70.
Discusses the notation, the techniques, and also several problems in Diophantus' Arithmetic. The author finds that Diophantus' methods are similar to those of the Babylonians, and observes that "the work may be viewed as an episode in the decline of Greek mathematics or as the finest flowering of Babylonian algebra." One interesting problem seems to involve an approximation to a square root. Swift also discusses the transmission of Diophantus' work and the resurgence of interest in it in the 1500s and 1600s. There doesn't seem to have been much interest in it in the Hindu or Islamic world. Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: Diophantus, Diophantine Equations, and Sumerians and Babylonians.