The Pell equation, by Edward Everett Whitford.

THE PELL EQUATION

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A7, show that
pn = rqn - qn-, "
Mathematical questions from the Educational Times, vol.
XXX, p. 49, London, 1879.
This theorem gives a ready method of finding x, when
y has been found in the equation
x2- Ay2 = 1.
L. RODET, "Sur une methode d'approximation des
racines carrees connue dans l'Inde anterieurement a la
conquete d'Alexandre," Bulletin de la Societe Mathematique de France, vol. VII, p. 98, Paris, 1879.
The author thinks that the rule of Baudhayana is the
foundation of Newton's method.
T. PEPIN, "Sur quelques equations indeterminees du
second degre et du quatrieme," Atti della Accademia pontificia de' Nuovi Lincei, vol. XXXII, p. 79, Rome, 1879.
C. HENRY, " Sur une valeur approchee de 2 et deux
approximations de 3d3," Bulletin des sciences mathematiques, vol. III (2), p. 515, Paris, 1879.
LIONET, F. PISANI, "A question on the solution of
x2 + 1 = 2y2," Nouvelles annales de mathematiques,
vol. XVIII (2), p. 528, vol. XX (2), p. 373, Paris, 1879,
1881.
The question concerns the law of recurrence in the
solution; for example
Xn = 6Xn-l - Xn-2.
S. REALIS, "Sur quelques questions se rattachant au
probleme de Pell," Nouvelle correspondance mathematiques, vol. VI, p. 306, p. 342, Paris, 1880.
These articles give a method of deducing the chief
formulas which relate to this problem and show that these
formulas are capable of extension.