By a mistake of Euler, the Diophantine equation y^2 - Ax^2 = 1
has been erroneously known as "Pell's equation"; but, in fact,
the English mathematician John Pell (1611-1685) did no more than
copy it down in his papers, from Fermat's letters of 1657 and
1658. For an extensive historical account on "Pell's equation",
see Sir Thomas L. Heath, Diophantus of Alexandria : A Study in
the History of Greek Algebra (Dover Pub., New York, 1931-1963,
552 pages), Supplement, Section II: "Equation y^2 - Ax^2 = 1,
pp. 277-292. Particularly in page 285, after a presentation of
the history of the equation up to Fermat's time (including
citations to Pythagoreans, Archimedes, Diaphanous, and the
Indian solution), one can read that: " ... Fermat rediscovered
the problem and was the first to assert that the equation x^2 -
Ay^2 = 1, where A is any integer not a square, always has an
unlimited number of solutions in integers. His statement was
made in a letter to Frénicle of February, 1657 (cf. Oeuvres de
Fermat, II, pp.333-4). Fer