The Pell equation, by Edward Everett Whitford.

THE PELL EQUATION

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directly furnish the solution of the equation
x2 - Ay2 = - 1,
when possible. The case in which the first transformation
is by an inferior limit and succeeding ones by superior
limits is discussed. The author, before he wrote his
article, did not know of the papers of M. A. Stern and B.
Minnigerode. This is an example of how valuable the
work of the historian of mathematics could be.
WEILL, "Sur quelques equations indeterminees," Nouvelles annales de mathematiques, vol. IV (3), p. 189,
Paris, 1885.
General formulas for the solutions of the equations
X2 - Ay2 = N2
and
2 - Ay2 = 1
are discussed.
H. VAN AUBEL, "Quelques notes sur le probleme de
Pell," Association frangaise pour l'avancement des sciences, compte rendu, part 2, p. 135, Paris, 1885.
This article gives the general form for the solution in
terms of the convergents found near the middle of the
period of the continued fraction. It gives methods of
finding the solution of the equation
2 - Ay2 = 1
quickly for many particular values of A.
G. FRATTINI, "Intorno ad un teorema di Lagrange,"
Atti della Reale Accademia dei Lincei, rendiconti, vol. I,
p. 136, Rome, 1885.
There are many theorems upon the solvability of the
congruence,
x2 -Dy2 X (mod p).
H. RICHAUD, "Solution of the equation
y2 - 1549x2 = - 1,"