The Pell equation, by Edward Everett Whitford.

162 THE PELL EQUATION
APPENDIX A.
The following table gives the development of 4A into
a continued fraction for non-square values of A from
A = 1,501 to A = 2,012.
The development is periodic, the period beginning with
the second term. The last term of the period is always
double the first term of the development. The period is
symmetric. The next to the last term equals the first,
the third from the last equals the second, and so on.
Then only the first half of the period need be written.
To indicate its position in the period, the term that completes the first half is written in parentheses. When
however the number of terms is odd, the middle term and
the one preceding it are enclosed in parentheses. Under
each term a number is written which is the absolute value
of the form x2 - Ay2 when x/y is the convergent corresponding to that point in the development of the continued fraction. These values are alternately positive
and negative. The 1 which would always come under the
first term of the continued fraction is omitted.
Example,
41,512 = 38 + -1,512 - 38,
1 1,512 + 38 41,512 - 30
1,512 - 38 68 1 68
68 _1,512 + 30 41,512 - 33
41,512- 30 9 9
9 _ 11,512 + 33 41,512 - 14
41,512 - 33 47 47
47 _ 1,512 + 14 41,512 - 14
1,512 -14 28 = 1+ 28
l1,512- 14 28 28