The Pell equation, by Edward Everett Whitford.

118

THE PELL EQUATION

Tables of such factors are given for various values of
f and g up to f = 17, g = 89.
H. J. S. SMITH, "Report on the theory of numbers,"
British Association report, p. 292, London, 1861; "Collected Mathematical papers," vol. I, p. 163, Oxford, 1894.
This treatise contains many theorems relating to the
Pell equations T2 - DU2 = 1 and T2 - DU2 = 4.
C. RICHAUD, "Enonc6s de quelques theoremes sur la
possibilite de l'equation x2 - Ny2 = - 1 en nombres
entiers," Journal de mathematiques pures et appliquees,
vol. IX (2), p. 384, Paris, 1864.
C. RICHAUD, "Demonstrations de quelques theoremes
concernant la resolution en nombres entiers de l'equation
x2- Ny2 = - 1," Journal de mathematiques pures et
appliquees, vol. X (2), p. 235, Paris, 1865.
C. RICHAUD, "Sur la resolution des equations
2- Ay2 = 2,1,"
Atti dell' Accademia pontificia de' Nuovi Lincei, vol.
XIX, p. 177, Rome, 1865.
C. RICHAUD, "Sur l'equation x2 - Ny2 = -," Journal
de mathematiques pures et appliquees, vol. XI (2), p. 145,
Paris, 1866.
These articles of Richaud contain many theorems on the
solvability of the equation x2 - Ny2 = - 1, depending
on whether or not the different factors of N are quadratic
residues of each other.
E. CATALAN, "Rectification et addition a la note sur un
probleme d'analyse indeterminee," published in Atti dell'
Accademia pontificia de' Nuovi Lincei, vol. XX, p. 1,
Rome, 1867, Atti dell' Accademia pontificia de' Nuovi
Lincei, vol. XX, p. 77, Rome, 1867.
This note is upon the equation
Ax2 - By2 = 1.