Quadratic Diophantine Equation x(2) - (t(2) - t)y(2) - (4t-2)x + (4t(2)-4t)y=0

Ozkoc A., TEKCAN A.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.33, no.2, pp.273-280, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 2
  • Publication Date: 2010
  • Title of Journal : BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • Page Numbers: pp.273-280

Abstract

Let t >= 2 be an integer. In this work, we consider the number of integer solutions of Diophantine equation D : x(2) - (t(2) - t)y(2) - (4t - 2)x + (4t(2) - 4t)y = 0 over Z. We also derive some recurrence relations on the integer solutions (x(n), y(n)) of D. In the last, section, we consider the same problem over finite fields F-p for primes p >= 5.