The Pell equation, by Edward Everett Whitford.

THE PELL EQUATION

149

con una nota sull' equazione di Pell," Periodico di matematica, vol. I (3), p. 57, Leghorn, 1904.
In introducing the concept index, meaning the maximum number of factors of an irrational binomial, the
author solves by a new method the equation
x2 - Dy2 = N
in the case where D is an integer or a polynomial of even
degree.
A. S. WEREBRUSOW, "Solution de x2 - Ay2 = - 1,"
L'Intermediare des mathematiciens, vol. XI, p. 154, 242.
Paris, 1904.
G. FRATTINI, "Nota sull' equazione di Pell," Periodico
di matematica, vol. XIX, p. 71, Leghorn, 1904.
R. W. D. CHRISTIE, A. CUNNINGHAM, "To find an
infinity of positive integral values of X which belong to
the same Y in the Pellian equation Xn2 - PY = - 1,"
Mathematical questions from the Educational Times,
vol. VII (2), p. 79, London, 1905.
Example,
702 - 293 132 = 74 - 1,.
R. W. D. CHRISTIE, A. H. BELL, A. CUNNINGHAM,
"Solve X2 - 19Y2 = - 3 in integers by the use of other
convergents than the ordinary Pellian," Mathematical
questions from the Educational Times, vol. VIII (2), p.
28, London, 1905.
Use is made of Euler's theorem extended, of the negative
development of 1/19, and of the triple series of Bell.
A. CUNNINGHAM, "(1) Factorize into prime factors
N = (70,600,7342 + 1). Here N = qp2 where p is a
large prime, (2) Show how to find very large numbers
(> 1050) of the form N = y2 + 1 = qm2 where m is very
large (> 1025)," Mathematical questions from the Educational Times, vol. VIII (2), p. 83, London, 1905.