The Pell equation, by Edward Everett Whitford.

116

THE PELL EQUATION

L. WANTZEL, " Divisors of numbers of the form x2 - cy2,
Extraits des Proces-Verbaux des seances de la Societe
Philomathique, p. 19, Paris, 1848.
J. B. LUCE, "On the theory of numbers," American
Journal of science and arts, vol. VIII, p. 55, New Haven,
1849.
Application is made to the solution of p2 - nq2 = 1 for
many special values of n. A table is given for reducing
the numbers n up to n = 158 when considered "complex"
for purposes of the solution, to "simpler" numbers by
multiplying by a square factor.
F. ARNDT, "Untersuchungen fiber einige unbestimmte
Gleichungen zweiten Grades, und fiber die Verwandlung
der Quadratwurzel aus einem Bruche in einen Kettenbruch," Archiv der Mathematik und Physik, vol. XII,
p. 211, Grtfswald, 1849.
This article closes with a table of the fundamental
solutions of p02 - p''2 = 1 and p92 - pl02 = 2 from
pp' = 3 to pp' = 1,003.
P. TCHEBICHEFF, "Sur les formes quadratiques,"
Journal de mathematiques pures et appliquees, vol. XVI,
p. 257, Paris, 1851.
The whole treatise is a discussion of the equations
x2 -Dy2 = N.
P. VOLPICELLI, "Alcune ricerche relative alla teorica
dei numeri, "Atti dell' Accademia pontificia Nuovi Lincei,
vol. VI, p. 77, Rome, 1852.
A. G6PEL, "De aequationibus secundi gradus indeterminatis," Journal fiir die reine und angewandte Mathematik, vol. XLV, p. 1, Berlin, 1853.
The general equations x2 - Ay2 = i C are discussed,
with such questions as for what values of A is the equation
2 - Ay2= + 2
solvable.