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Solvability Characterizations Of Pell Like Equations, Jason Smith

Boise State University Theses and Dissertations

Pell's equation has intrigued mathematicians for centuries. First stated as Archimedes' Cattle Problem, Pell's equation, in its most general form, X² – P • Y² = 1, where P is any square free positive integer and solutions are pairs of integers, has seen many approaches but few general solutions. The eleventh century Indian mathematician Bhaskara solved X² – 61 • Y² = 1 and, in response to Fermat's challenge, Wallis and Brouncker gave solutions to X² – 151 • Y² = 1 and X² –313 • Y² = 1. Fermat claimed to …