The Pell equation, by Edward Everett Whitford.

THE PELL EQUATION

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can be obtained from the following formulas,
(a2 rn m)2 - (a2 2m)a2 = m2,
(na2: m)2 - (n2a2 = 2nm)a2 = m2,
(a, m, n = 1, 2, 3, *. )).
H. W. L. TANNER, "Notes on the automorphs of
binary quadratic forms," Messenger of mathematics,
vol. XXIV, p. 180, London, 1895.
Attention is drawn to the essential identity of automorphs with the theory of units in the generalized theory
of numbers. The relation of the Pell equation to the
automorph is thus more clearly shown.
C. J. DE LA V. POUSSIN, "Sur les fractions continues et
les forms quadratiques," Annales de la Societe Scientifiques de Bruxelles, vol. XIX, p. 111, Brussels, 1895.
The author points out the advantage of the continued
fractions of which all the partial quotients after the first
are negative integers.
G. FRATTINI, "Dell equazione di Pell a coefficiente
algebrico," Giornale di matematiche di Battaglini, vol.
XXXIII, p. 371, vol. XXXIV, p. 98, Naples, 1895, 1896.
This is a treatise on the equation x2 - Ay2 = 1 in which
A is an integral function of u, thus
x2 - (au2 + bl + c)y2 = 1.
G. SPECKMAN, "Uber unbestimmte Gleichungen xten
Grades," Archiv der Mathematik und Physik, vol. XIV
(2), p. 443, Leipzig, 1896.
From the consideration of the solutions of the Pell equation of the second degree, T2 - DU2 = 1, formulas are
produced for the solution of the equation
TX -DUx = m2.
A. PALMSTROM, "Quelques proprietes des solutions de
certaines equations indeterminees de deuxieme degre,"
Aarbog, 1896.