JP Journal of Algebra, Number Theory and Applications
Volume 2, Issue 1, Pages 21 - 46
(April 2002)
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INTEGRAL REPRESENTATIONS AND SOME EXPLICIT
EVALUATIONS OF A CONTINUED FRACTION OF RAMANUJAN
S. N. Arteha (Russia)
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Abstract: Using the representation of
numbers, the methods of decreasing the number of
calculation steps for Pell’s equation are developed.
The formulae relating the natural solution x0
of Pell’s equation for A0 with
the infinite number of minimal natural solutions
xi for other Ai are
obtained for various cases. The parametric
representation of Pell’s equation solutions are
obtained with the help of new "method of hidden
parameters". |
Keywords and phrases: Diophantine equations,
Pell’s equation, continued fractions. |
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