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Published online by Cambridge University Press: 20 January 2009
This is a note on the theory of continued fractions, in which the chief feature is the use made of the successive remainders or divisors which occur in the reduction of any given ratio to a continued fraction.
The treatment of the Pellian equation also differs from that which is generally given.
* For the theory, see, for instance, Chrystal's Algebra, chapters 32, 33.
† Hence √N − a is positive, that is, a must be <√N or else negative: in the former case x/y is a convergent, ordinary or intermediate, to √N.
* Since Am−2=amAm−1+Am and Am−1 > Am it follows that Am<½Am−2.
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