The Pell equation, by Edward Everett Whitford.

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THE PELL EQUATION

E. PICARD, "Sur les formes quadratiques binaires a
indeterminees conjugees," Comptes rendus de l'Academie,
vol. XCVI, p. 1567, Paris, 1883.
This article gives a general method of solving a generalized Pellian equation
xxo - Dyyo = 1.
DE ROQUIGNY, JAMET, BROCARD, EVEN, "Quels sont
les polygons dont le nombre des diagonales est un carre?"
Mathesis, vol. III, p. 216, vol. VI, p. 162, Paris, 1883, 1886.
This is solved by the aid of the Pell equation
(2v - 1)2 - 8u2 = 1.
The results are 6, 27, 150, 867, *.
E. MAHLER, "Die Irrationalitaten der Rabbinen,"
Zeitschrift fir Mathematik und Physik, historischliterarische Abteilung, vol. XXIX, p. 41, Leipzig, 1884.
M. D'OCAGNE, "Sur l'6quation indeterminee
x2 _ ky2 = z2,
Comptes rendus de l'Academie, vol. XCIX, p. 1112,
Paris, 1884.
The solutions are stated by the aid of a certain function
s(oa, 0, n), and are given without proof.
H. WEISSENBORN, "Die irrationalen Quadratwurzeln
bei Archimedes und Heron," Berlin, 1884.
S. ROBERTS, "Notes on the Pellian equation," Proceedings of the London Mathematical Society, vol. XV,
p. 247, London, 1884.
The author shows that if we take the nearest integer
limit in the development of a continued fraction a form
will be arrived at whose coefficient is unity. This method
sometimes gives a shorter solution than the usual method
of always taking the inferior limit. The use of superior
limits alone may prolong the operation, and does not