Studying Pell's Equation by Using the Quadratic Orders
published by Tishreen University
in 2018
in Mathematics
and research's language is
العربية
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Abstract in English
In this paper , we will study the ability to solve Pell's equation in the
set Z, we give necessary and sufficient conditions to solve this equation , depending on the
ideals in orders of the real quadratic fields .We also introduce the formula of the opposite
ideal for every solution of this equation , in special cases.
References used
ANDREESCU, T., ANDRICA, D., Quadratic Diophantine Equations, Springer, New York, London, 2015
BOLKER, E. D. Elementary Number Theory, An Algebraic Approach, W. A. Bedjamin, Inc. New York, 1970
COVILL. E., JAVAHERI, M., KRYLO. N., On the Subgroup Generated by Solutions of Pell’s Equation, Arxiv: 1609.00440vol.1, math. NT, 2Sep,2016