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A Comprehensive Course in Number Theory by Alan Baker

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8

Diophantine equations

8.1 The Pell equation

Diophantine analysis has its genesis in the fertile mind of Fermat. He had studied Bachet’s edition, published in 1621, of the first six books that then remained of the famous Arithmetica; this was a treatise, originally consisting of 13 books, written by the Greek mathematician Diophantus of Alexandria at about the third century AD. The Arithmetica was concerned only with the determination of particular rational or integer solutions of algebraic equations, but it inspired Fermat to initiate researches into the nature of all such solutions, and herewith the modern theories began.

An especially notorious Diophantine equation, in fact the issue of a celebrated challenge from Fermat to the English mathematicians ...

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