The Pell equation, by Edward Everett Whitford.

128

THE PELL EQUATION

S. ROBERTS, "Notes on a problem of Fibonacci's,"
Proceedings of the London Mathematical Society, vol.
XI, p. 35, London, 1880.
This problem is to find x, y, v, u, for a given P in the
equations
x2 + Py2 = u2 and x2 - Py2 = v2.
S. ROBERTS, "Note on the integral solution of
2 - 2Py2 = - 2 or - 2z2
in certain cases," Proceedings of the London Mathematical
Society, vol. XI, p. 83, London, 1880.
A. KUNERTH, "Berechnung der ganzzahligen Wurzeln
unbestimmter quadratischer Gleichungen mit zwei unbekannten aus den fur letztere gefunden Briichen, nebst
den Kriterien der Unm6glichkeit einer solchen Losung,"
Situngsberichte der kaiserlichen Akademie der Wissenschaften, mathematisch-naturwissenschaftliche Classe, vol.
XXXII (Abtheilung 2), p. 342, Vienna, 1880.
P. TANNERY, "Sur le probleme des boeufs d'Archimede," Bulletin des sciences mathematiques, vol. V (2),
p. 25, Paris, 1881.
P. TANNERY, " L'arithmetique des Grecs dans Pappus,"
Memoires de la Societe des Sciences physiques et naturelles
de Bordeaux, vol. III (2), p. 351, Paris, 1881.
Plato considered the equations 2y2 - x2 = - 1; Archimedes in his "Circle Measure" the equations
3y2 x2 = -1 and 3y2 x2 = 2.
Diophantus was essentially influenced by Heron and
Hypsicles. New conclusions are drawn from the "Cattle
Problem" of Archimedes making it clear that an indeterminate analysis of no inconsiderable extent existed before
the time of Christ.
P. TANNERY, "L'arithmetique des Grecs dans Heron
d'Alexandrie," Memoires de la Societe des Sciences