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An Algorithm for Explicit Form of Fundamental Units of Certain Real Quadratic Fields |
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PP: 23-27 |
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doi:10.18576/jant/040104
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Author(s) |
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Ozen Ozer,
Ayten Pekin,
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Abstract |
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| Quadratic fields have applications in different areas of mathematics such as quadratic forms, algebraic geometry, diophantine
equations, algebraic number theory, and even cryptography. The Unit Theorem for real quadratic fields says that every unit in the integer
ring of a quadratic field is given in terms of the fundamental unit of the quadratic field. Thus determining the fundamental units of
quadratic fields is of great importance. In this paper, we obtained an explicit formulation to determine the forms of continued fraction
expansion and fundamental units of certain real quadratic number fields where the period in the continued fraction expansion of the
quadratic irrational number of the certain real quadratic fields is equal to 7 by using a practical algorithm for special cases. Moreover,
a part of this paper is generalize and complete [2]. |
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