published by Damascus University
in 2012
in
and research's language is
العربية
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Abstract in English
In this work, we studied Pell equations X2 - DY2 = ±2. We showed when both
of these equations are solvable, and we found the necessary and sufficient
condition for the solubility of each one by the continued fractions and the
concept of the central norm.
References used
Burton, D. M. 1994. Elementary Number Theory, Second Edition. Kaplana Press, Delhi
Mollin, R. A. 2005. Lagrange, central norms, and quadratic Diophantine equation, Internat. J. Math. and Math. Sci, v.7, pp. 1039 - 1047
Mollin, R. A. 1996. Quadratics, CRC Press, Boca Raton, New York, London, Tokyo