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

Ozkoc A., TEKCAN A., CANGÜL İ. N.

APPLIED MATHEMATICS AND COMPUTATION, cilt.218, sa.3, ss.703-706, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 218 Sayı: 3
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/j.amc.2011.03.071
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.703-706
  • Anahtar Kelimeler: Diophantine equation, Pell equation, Integer solutions, Continued fraction, Finite fields
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.