The Pell equation, by Edward Everett Whitford.

THE PELL EQUATION

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and of
x2 - Ay2 = 1
are given, the smaller set, of course, being the solution of
x2 - Ay2 = - 1.
In fact, it is worthy of notice that the fundamental
solution of
x2 - Ay2 = 1
occurs last and is precisely the most complicated of all
the fundamental solutions of the form
x2- Ay2 = B
when such solutions exist at all.
If -A is developed into a continued fraction, we have
WA = k + 1
k2+
k+ k2 ------
kl +or, as it might be written,
-A = (k, ki, k2, *., k2, ki, 2k, *.).
Let us now take for two model examples A = 1,953 and
A = 1,546. Then.1,953 = (44, 5, 5, 3, (12), 3, 5, 5, 88, *..),
1, 17, 16, 27, (7), 27, 16, 17, 1,...,
Y1,546= (39, 3, 7, (1), (1), 7, 3, 78,.-.),
1, 25, 10, (39), (39), 10, 25, 1,...,
and we construct tables in the manner described.