JP Journal of Algebra, Number Theory and Applications
Volume 1, Issue 1, Pages 57 - 75
(April 2001)
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QUADRATIC DIOPHANTINE EQUATIONS DETERMINED BY CONTINUED
FRACTIONS
R. A. Mollin (Canada)
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Abstract: The
purpose of this article is to use the theory
of continued fractions in conjunction with
ideal theory (called the infrastructure) in
real quadratic fields to provide criteria for
the solutions of certain quadratic Diophantine
equations and link all of this to certain new
Jacobi symbol identities. This continues work
in [Acta Arith. 85 (1998), 331-349] and [Canad.
Math. Bull. 43 (2000), 218-225]. |
Keywords and phrases: continued
fractions, Diophantine equations, quadratic irrationals,
ideals, Jacobi symbols. |
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