JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 1, Pages 85 - 120
(April 2003)
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THE
DIOPHANTINE EQUATION x2 –
Dy2 = N, AND
CONTINUED FRACTIONS
Franz Halter-Koch (Austria) and Maximilian Pacher (Austria)
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Abstract: We consider
the diophantine equation
for those values of D which are
represented by the principal form of
discriminant N or 4N. In this
case, the infrastructure of the class group of
contains signals announcing solutions of
the diophantine equation. The results are
finally interpreted in terms of continued
fractions. |
Keywords and phrases: Pell’s equation, quadratic orders, continued
fractions. |
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