The Pell equation, by Edward Everett Whitford.

THE PELL EQUATION

155

between 1,501 and 2,000 there are 38 values for which the
equation
x2 - Dy2 = 1
is solvable.
E. MALO, "Solution de l'6quation
x2- Dy2 = - 1,
L'Intermediare des mathematiciens, vol. XIII, p. 246,
Paris, 1906.
Several cases are discussed. The equation is impossible if
D = 4u2 2 2,
possible if
D = 2[u2 + (u2 + 1)] or (2u + 1)2 + 4.
M. VON THIELMANN, "Die Zerlegung von Zahlen mit
Hilfe periodischer Kettenbriiche," Mathematische Annalen, vol. LXII, p. 401, Leipzig, 1906.
Upon the ground of the period of the continued fraction
of ik a Pellian equation is formed whose solution makes
it possible to find the so-called type of the given number
k, according to which the separation follows easily when
possible.
A. CUNNINGHAM, "High Pellian factorisations," Messenger of mathematics, vol. XXXV (2), p. 166, London,
1906.
Under the designation "Pellian factorisations" is
understood such separation of numbers N of the form
N = x2 + 1 into factors as are easily worked out from
the known solutions of the Pell equation. The existing
tables of the solutions of the Pell equation give at first
glance the separation of a considerable number of very
large numbers N. These numbers are called Pellian
numbers. This article shows the factorization of N up
to 78 figures.
R. W. D. CHRISTIE, A. H. BELL, "Having given
n2 - pyn2= 1 to find a multiplier giving successive values,