The Pell equation, by Edward Everett Whitford.

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THE PELL EQUATION

P. TANNERY, Review of "Geschichte der Gleichung
t2 - Du2 = 1," by H. Konen, Bulletin des sciences mathematique, vol. XXVII (2), p. 47, Paris, 1903.
A HOLM, "On the convergents to a recurring continued
fraction with application to find integral solutions of the
equation x2 - Cy2 = (- 1)nDD," Proceedings of the
Edinburgh Mathematical Society, vol. XXI, p. 163,
London, 1903.
The solutions of the above equation are furnished by,
(1), when c the number of quotients in the cycle of i/C
is even,
x - y XC = (pn - qn ]C)(pc -q sC)
where pn, qn, is a solution of the equation
x2 - Cy2 = Dn.
n any integer, pc, qC, is the fundamental solution of the
equation x2 - Cy2 = 1, m any integer or 0; (2) when c is
odd,
x - Y XC = (pn, - qn C) (p - qc WC)2n,
m any integer or 0.
RUDIS, WEREBRUSOW, BESOUCLEIN, "Solution de lequation x2 - Dy2 = - 1," L'Intermediare des math6 -maticiens, vol. X, p. 102, p. 224, Paris, 1903.
G. DE LONGCHAMPS, "Equation x2 - Dy2 = - 1,"
L'Intermediare des mathematiciens, vol. X, p. 319, Paris,
1903.
E. B. ESCOTT, A. WEREBRUSOW, "The necessary relations between the integers, a, b, c, * * in order that the
expression
[a, b, c,.. c, b, a]
[b, c,...c, b]
where fN = (a, b, c,... c, b, 2a,...), be an integer,"
L'Intermediare des mathematiciens, vol. X, p. 97, 318,
vol. XI, p. 154, Paris, 1903, 1904.