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Solving some parametric quadratic Diophantine equation over Z and F-p
Journal article   Peer reviewed

Solving some parametric quadratic Diophantine equation over Z and F-p

Arzu Ozkoc, Ahmet Tekcan and Ismail Naci Cangul
Applied mathematics and computation, Vol.218(3), pp.703-706
01/10/2011
DOI: https://doi.org/10.1016/j.amc.2011.03.071

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
Let t >= 2 be an integer. In this work, we consider the integer solutions to the Diophantine equation D: x(2) + (t - t(2))y(2) + (4 - 8t)x + (8t(2) - 8t)y + 3 = 0 over Z and over finite fields F-p for primes p >= 2, respectively. We also derive some algebraic identities related to the integer solutions of D including recurrence relations and continued fractions. (C) 2011 Elsevier Inc. All rights reserved.

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