The Pell equation, by Edward Everett Whitford.

THE PELL EQUATION

123

S. BILLS, "A new method of solving in integers the
equation x2 - Ay2 = 1= I," Mathematical questions from
the Educational Times, vol. XXIII, p. 98, London, 1875.
BOOTH, "Find the law which gives the value of t so as
to make nt2 =t k a square," Mathematical questions from
the Educational Times, vol. XXIII, p. 99, London, 1875.
A. B. EVANS, HART, "Find the least integral values of
x, y, that will satisfy the equation x2 - 953y2 = = 1,",
Mathematical questions from the Educational Times,
vol. XXIII, p. 107, London, 1875.
A. MARTIN, "Correction of an error in Barlow's Theory
of numbers," Analyst, vol. II, p. 140, Des Moines, 1875.
S. BILLS, A. MARTIN, G. HART, A. B. EVANS, "Solution
of a question," Mathematical questions from the Educational Times, vol. XXIII, p. 109, vol. XXIV, 9, 109,
London, 1875, 1876.
If R is an integral value of y which makes Ay2 + 1 a
square and r is the smallest integral value of y which makes
Ay2 - 1 a square, then R is a multiple of r.
A. MARTIN, HART, "Find the least integral values of
x and y that will make x2 - 5,693y2 = - 1," Mathematical questions from the Educational Times, vol. XXV, p.
97, London, 1876.
A. MARTIN, "On the equation x2 - 5,658y2 = 1 in
Barlow's Theory of numbers, p. 299," Mathematical questions from the Educational Times, vol. XXVI, p. 87,
London, 1876.
H. J. S. SMITH, "Notes on the theory of the Pellian
equation and of binary quadratic forms of a positive
determinant," Proceedings of the London Mathematical
Society, vol. VII, p. 196, London, 1876, "Collected
papers," vol. II, p. 148, Oxford, 1894, "Collectanea
Mathematica," p. 117, Milan, 1881.
This article contains the theorem that T + U - is