The Pell equation, by Edward Everett Whitford.

THE PELL EQUATION

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BIBLIOGRAPHY.
P. COSALI, "Origine, trasporto in Italia, primi progressi in essa dell' algebra," vol. I, p. 146, Parma, 1798.
The work of Lagrange and Euler upon the equation
AY2 + B = Z2 and its connection with the general
indeterminate equation of the second degree in two unknowns is discussed.
F. PEZZI, "Nuovi teoremi sulla posibilita' dell' equazione x2 - Ay2 = -= 1 e ricera del numero de' termini
del periodo della radice quadra di un numero non quadrato, sviluppata in frazione continua," Memorie di
matematica e di fisica della Societa Italiana delle Scienze,
vol. XIII, p. 342, Modena, 1807.
The author proves that x2 - Ay2 = 1 is always solvable, that x2- Ay2 = - 1 is solvable in integers if
the number of terms in the period of the continued fraction
in the development of i/A is odd, impossible if the number
of terms is even. There are four theorems about the
results in solving the equation Mn2 = ANn2 + ( - )n
according as A,, N,, M,, are odd or even. Complete
examples are given for A = 94 and A = 1,005.
KRAMP, "Recherches sur les fractions continues
periodiques," Annales de mathematiques pures et appliquees, vol. I, p. 261, Nimes, 1810 and 1811.
Application is made to the equation lly2 + 49 = x2
(p. 283); and this particular equation is treated more
fully by Dr. Kramp in another communication in the
same journal (p. 319).
TEDENAT, "Communiquee aux redacterus des Annales
sur la lettre de M. Kramp," Annales de mathematiques
pures et appliquees, vol. I, p. 349, Nimes, 1810 and 1811.
This article gives the formulas for the solution of the
equation y2 - Ax2 = B, obtained from the integration
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