The Pell equation, by Edward Everett Whitford.

138

THE PELL EQUATION

The author discusses the law of recurrence which
connects the different solutions of the Pell equation.
C. ST6RMER, "Om en egenskab ved losningerne af den
Pellske ligning x2 - Ay2 = - 1," Nyt Tidsskrift for
Mathematik, vol. VII, p. 49, Copenhagen, 1896.
The following theorem is found: if x and y are positive
roots of the equation x2 - Ay2 = - 1, and a, b, the
smallest among these roots, then
1 1 a
tan-' - tan-' = 2 tan-'
X2 n-1 X2n+l X2n
and
1 1 b
tan-1 + tan- = 2 tan-1-.
X2n-1 X2 nl1 Y2 n
C. STORMER, A. PALMSTROM, To solve in integers
1 + x2 = 2y4, L'Intermediare des mathematiciens, vol.
III, p. 197, vol. IV, p. 89, Paris, 1896, 1897.
Solutions are found by the aid of the Pell equation.
A. BELIGNE, H. BROCARD, "Solution of
X2 + (X + 1)2 = y4
L'Intermediare des mathematiciens, vol. IV, p. 214, Paris,
1897.
R. FRICKE, FELIX KLEIN, "Vorlesungen fiber die
Theorie der elliptischen Modulfunctionen," vol. I, p. 253,
Leipzig, 1897.
M. CURTZE, "Quadrat- und Kubikwurzeln bei den
Greichen nach Herons neu aufgefunden MerTpLK&," Zeitschrift fir Mathematik und Physik, Historisch-literarische
Abteilung, vol. XLII, p. 113, Leipzig, 1897.
M. CURTZE, "Die Quadratwurzelformel des Heron bei
Regimontan und damit Zusammenhangendes," Zeitschrift
fur Mathematik und Physik, Historisch-literarische Abteilung, vol. XLII, p. 145, Leipzig, 1897.