The Pell equation, by Edward Everett Whitford.

THE PELL EQUATION

119

M. A. STERN, "Uber die Eigenschaften der periodischen
negativen Kettenbriiche welche die Quadratwurzel aus
einen ganzen positiven Zahl darstellen," Abhandlungen
der Konigliche Gesellschaft der Wissenschaften, vol. XII,
p. 3, Gottingen, 1866.
In the continued fractions - 1 is used for the numerators.
J. FRISCHAUF, in Situngsberichte der mathematischnaturwissenschaftlichen Classe der Kaiserlichen Akademie
der Wissenschaften, vol. LV (Abtheilung 2), p. 121,
Vienna, 1867.
P. SEELING, "Uber die Formen der Zahlen, deren
Quadratwurzeln in Kettenbriichen dargestellt, Perioden
von einer gewissen Anzahl Stellen haben," Archiv der
Mathematik und Physik, vol. XLIX, p. 4, Griefswald,
1869.
This article contains tables for continued fractions with
periods of from one to seven numbers, and for continued
fractions for /IA for all values of A up to A = 602. It
also discusses the forms of A for which
x2 - Ay2 = 1.
L. OTTINGER, "Uber das Pell'sche Problem und einige
damit zusammenhangende Probleme aus der Zahlenlehre,"
Archiv der Mathematik und Physik, vol. XLIX, p. 193,
Griefswald, 1869.
Formulas for the general solutions of the equations
x2-Ay2 = - 1 are given. If x2 - Ay2 = ==b is solvable, and if p, q, is one solution, and t, u, is a solution of
the Pell equation so that
p2 - Aq2 = 2 b
and
t2 - Au2 = 1,
then x = pt = Aqu and y = pu - qt. Tables of solutions