The Pell equation, by Edward Everett Whitford.

158

THE PELL EQUATION

For the cases n = 2, 3, 4, this equation leads to problems
of the invariant theory.
G. CORNACCHIA, "Sulla risoluzione in numeri interi
dell' equazione x" -qyn = 1," Revista di fisica,
matematica e scienze naturali, vol. VII (2), p. 221,
Pavia, 1907.
If the equation possesses an integral solution x, y, then
x/y is a convergent of 1q developed into a continued
fraction.
AURIC, "Sur le developpement en fraction continue
d'une irrationnelle ambigue du second degre," Bulletin
de la Societe Mathematique de France, vol. XXXV,
p. 121, Paris, 1907.
The discussion depends upon the Pell equation
t - Du2 = 4
R. W. D. CHRISTIE, A. H. BELL, "Find, by the quintic
roots of minus unity, all the values in succession of x, y,
in the equation x2 - 5y2 = - 4," Mathematical questions from the Educational Times, vol. XIII (2), p.
35, London, 1908, Educational Times, vol. LX, p. 353,
Aug. 1, 1907, London.
x = (w2 + CO3)2n + (C4 + c5)2n = 3, 7, 18, *.,
(CO2 + 23)n2 - (W4 + WC5 )2n
Y (C(02 + C03) - (C4 +- ) - 1 '
R. W. D. CHRISTIE, T. STUART, A. CUNNINGHAM,
"Let x2 - py2 = 1, where p is of the form 4m + 3,
then
(x\ (py - y + z
z )-P (P+ 1) )
z being (2py - p + 1)/(p + 1)," Mathematical questions
from the Educational Times, vol. XIV (2), p. 56, London,
1908.