The Pell equation, by Edward Everett Whitford.

THE PELL EQUATION
That indeterminate equation of the second degree in
two unknowns which is of the form
X2 - Ay2 = 1
has long been called the Pellian equation, or the Pellian
problem; and it has rarely been mentioned by any other
title. As will be shown, John Pell had but little to do
with it; and yet, to attempt to rename it would be like
trying to give another name to North America because
Vespucius was not its discoverer. In referring to this as
the Pellian equation, modern mathematicians have not
disregarded Fermat, Wallis, Brouncker, Gauss, and the
hundreds of others who have contributed to the history
of the subject, just as in permitting the reciprocity theorem
to bear the name of Legendre,1 the world has not failed
to recognize the work of Kronecker. If the name were
changed, however, then such expressions as Pellian convergents, Pellian terms, Pellian numbers, and Pellian
factorizations,2 all depending upon the connection of
Pell's name with the equation, would become illogical
and mere arbitrary designations.
The name originated in a mistaken notion of Leonard
Euler3 that John Pell was the author of the solution which
was really the work of Lord Brouncker. Euler in his
cursory reading of Wallis's algebra must have confused
1 T. Pepin, "Etude historique sur la theorie des residues quadratiques,"
Memorie dell' Accademia pontificia di' Nuovi Lincei, vol. XVI, p. 229,
Rome, 1900.
2 A. Cunningham, "High Pellian factorisations," Messenger of Mathematics, vol. XXXV (2), p. 166, London, 1906. (2) indicates second series.
3 P. H. Fuss, editor, "Correspondance mathematique et physique de
quelques celebres geometres du XVIIIieme siecle," letter IX of L. Euler
to C. Goldbach, Aug. 10, 1732, p. 37, St. Petersburg, 1843.

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