The Pell equation, by Edward Everett Whitford.

160

THE PELL EQUATION

A. CHATELET, "Sur un cas particulier de l'6quation de
Pell," Bulletin de mathematiques elementaires, vol. XIV,
p. 307, Paris, 1909.
The author shows that it is possible always to obtain
one solution of
x2 - Ay2 = 1.
R. W. D. CHRISTIE, JAGAT CHANDRA PAL, A. CUNNINGHAM, "Prove the following equations,
(PnPn+1)2 +- (2qnQn+i)2 = q2n+1 pnn+1 - 2ql7q = + 1,
where pn2 - 2q,2 = 1, hence show that an endless
number of equations can be formed such as
32 42 = 52, 202 212 = 292, * *
Mathematical questions from the Educational Times, vol.
XV (2), p. 74, London, 1909.
G. FRATTINI, "La nozione d'indice e l'analisi indeterminata dei polinomi interi," Atti del IV congresso internazionale dei matematici, vol. II, p. 178, Rome, 1909.
If D and N are integral polynomials in a, then if one
solution, a, a, of the Pell equation x2 - Dy2 = 1 is known,
all the solutions of the equation x2 - Dy2 = N can be
deduced, and by this means we obtain the notion of an
index of a binomial E + F AiD where E and F are rational
functions of a.
A. AUBRY, "L'oeuvre arithmetique d'Euler," L'Enseignement mathematique, vol. XI, p. 329, Paris, 1909.
G. FONTENE, "Sur un cas particulier de l'6quation de
Pell," Bulletin de mathematiques elementaires, vol. XV,
p. 65, Paris, 1910.
A. LEVY, "Sur un cas particulier de l'equation de Pell,"
and "Sur une application de l'equation de Pell," Bulletin
de mathematiques elementaires, vol. XV, p. 66, Paris,
1910.