The Pell equation, by Edward Everett Whitford.

THE PELL EQUATION

143

then Qn and Pn/ul give the solution, tn, u,, of the above
equation.
H. KONEN, "Geschichte der Gleichung t2 - Du2 = 1,"
Leipzig, 1901.
This work is well conceived and developed with talent.
It gives an especially fine account of the contest between
Fermat and the English mathematicians. A third of
the entire treatise is given over to the discussion of the
work of Lagrange. In the bibliography of twenty-four
references given at the close the following corrections
should be noted: A. Martin's article is in the Analyst,
vol. IV, p. 154 (1877), not in vol. V, p. 118; and the
article in vol. V, p. 118 (1878), is by D. S. Hart, "The
solution of an indeterminate problem." Meyer's article
should be dated 1887 not 1889, and Schmidt's 1874 not
1876. Speckman's two articles in the Archiv der Mathematik und Physik are on p. 327 and p. 330, 1895, not
on p. 216 and p. 130, 1894. Frattini's (not Trattini)
first. article is in volume XXXIII of the Giornale di
Matematiche, not vol. XXX. The list contains the
following references which I have not found elsewhere:
Berkhan, "Lehrbuch der unbestimmten Analytik," 2 Bd.,
Halle, 1855-1856, Bd. II, p. 121. E. Meissel, "Beitrag
zur Pellschen Gleichung h6herer Grade," Progr. der
Ober-Realschule zu Kiel, 1891. Pistor, "Uber die
Auflisung der unbestimmten Gleichung 2. Grades in
ganzen Zahlen," Programm, Hamm, 1833. G. W.
Tenner, "Einige Bemerkungen fiber die Gleichung
ax2 == 1 = y2," Programm, Merseburg, 1841.
G. RICALDE in L'Intermediare des mathematiciens, vol.
VIII, p. 256, Paris, 1901.
The identities
(k2n 1)2- n(k2n - 2)k2 = 1, n2 - (n2- 1) 12 = 1,
(2n2 + 1)2 - (n2 + 1)(2n)2 = 1,
(8n + 25)2 - (4n2 + 25n + 39).42 = 1,