The Pell equation, by Edward Everett Whitford.

140

THE PELL EQUATION

The above problem is solved by Emmerich and A.
Goulard, Mathesis, vol. VIII (2), p. 52, Paris, 1898. H.
Brocard adds a bibliographic note, op. cit., p. 112. Besides questions already referred to, see E. Catalan in
Nouvelle correspondance mathematiques, p. 194, Brussels,
1877, and p. 285, 1879; G. de Longchamps, Journal de
mathematiques elementaires, vol. VIII, p. 15, Paris, 1884;
E. Catalan, H. Brocard, A. Boutin, Journal de mathematiques speciales, vol. XVII, p. 23, 117, 139, Paris, 1893.
C. ST6RMER, Inquiry concerning tables of solutions of
the Pell equations x2 - Dy2 = =t 1, L'Intermediare des
mathematiciens, vol. IV, p. 123, Paris, 1897.
Particular inquiry is made for the equation
x2 _ Dy2 = -
where D = 28p1p2... pnql2q22 * qn2 in which 5 = 0 or 1
and the p's and q's are of the form 4n + 1.
E. B. ESCOTT, "Reply concerning tables of solutions of
Pell equations," L'Intermediare des mathematiciens, vol.
V, p. 276, Paris, 1898.
The writer mentions no solutions but refers to tables of
continued fractions in Martin's Mathematical magazine,
vol. II, No. 7, 1892. See the reference.
H. BROCARD, "Note bibliographique sur l'equation de
Pell," Mathesis, vol. VIII (2), p. 112, Paris, 1898.
A. BOUTIN, "Sur un equation de Pell," Mathesis, vol.
VIII (2), p. 159, Paris, 1898.
The equation discussed is
x2- (m2- l)y2 = 1,
particularly in the case
m = 2.
E. DE JONQUIERES, "Sur un point de doctrine dans la
theorie des formes quadratiques," Comptes rendus de
l'Academie, vol. CXXVI, p. 991, 1077, Paris, 1898.