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This report focuses on the square roots of
positive integers whose continued fraction expansions have
be such an integer. Then the continued fraction expansion of is given by
We are interested in the factorization of into where is the continued fraction expansion of a rational number and represents the continued fraction expansion of in reverse order.
For a thorough introduction to continued fractions and
concepts used in this report, see Justin Miller's report: Families
of Continued Fractions.