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Register a new userStudying Pell's Equation by Using the Quadratic Orders
دراسة معادلة بل باستخدام المرتّبات التّربيعيّة
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Tishreen University ورقة بحثية
Publication date
2018
fields
Mathematics
and research's language is
العربية
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Shamra Editor
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درسنا في هذا البحث قابليّة حلّ معادلة بل في مجموعة الأعداد الصّحيحة ، حيث أعطينا شرطاً لازما و كافياً لقابليّة حلّ هذه المعادلة بالإعتماد على الإيديالات في مرتّبات الحقول التّربيعيّة الحقيقيّة، كما أعطينا صيغة الإيديال المقابل لكلّ حلّ لهذه المعادلة و ذلك من أجل حالات خاصّة .
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
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