The Pell equation, by Edward Everett Whitford.

THE PELL EQUATION

151

of the equations
x2 - Ay2 = - 1,
with applications.
E. B. ESCOTT, "Solution de l'6quation x2 - Dy2 = - 1,"
L'Intermediare des mathematiciens, vol. XII, p. 53,
Paris, 1905.
If D = a2 + b2, it is a necessary but not a sufficient
condition for the solution of the equation x2 - Dy2 = - 1
that a or b be a quadratic residue of D. The equation
x2- 2,306y2 = - 1 has no solution although both 41 and
25 are quadratic residues of 2,306.
RUDIS, "Solution de l'6quation x2- Dy2 =- 1,
L'Intermediare des mathematiciens, vol. XII, p. 54,
Paris, 1905.
J. SANDIER, "Solution de l'equation x2 - Dy2 = - 1,"
L'Intermediare des mathematiciens, vol. XII, p. 249,
Paris, 1905.
This article contains seven theorems concerning the
solution of the equations x2 - Dy2 = = 1. To obtain
one solution of the equation x2 - Dy2 = N it is sufficient
to have one each of the equations x2 - Dy2 = pi, (i = 1,
2, 3,...), p; being the distinct prime factors of N.
J. SCHRiDER, "Eine Eigentiimlichkeit der Naherungswerte von /22," Archiv der Mathematik und Physik, vol.
IX (3), p. 206, Leipzig, 1905.
P. EPSTEIN, "Zu der Mitteilung von Herrn J. Schroder
iber die Naherungswerte von J2," Archiv der Mathematik und Physik, vol. IX (3), p. 310, Leipzig, 1905.
The results given are known from the theory of the Pell
equation. If the continued fraction
K=1+ —1
k +k+"
k +$