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


Ozkoc A., TEKCAN A., CANGÜL İ. N.

APPLIED MATHEMATICS AND COMPUTATION, vol.218, no.3, pp.703-706, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 218 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.1016/j.amc.2011.03.071
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.703-706
  • Keywords: Diophantine equation, Pell equation, Integer solutions, Continued fraction, Finite fields
  • Bursa Uludag University Affiliated: Yes

Abstract

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.