Integer Solutions of a Special Diophantine Equation


Ozkoc A., TEKCAN A.

International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Halkidiki, Greece, 19 - 25 September 2011, vol.1389 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1389
  • Doi Number: 10.1063/1.3637759
  • City: Halkidiki
  • Country: Greece

Abstract

Let t not equal 1 be an integer. In this work, we determine the integer solutions of Diophantine equation D : x(2) + (2-t(2))y(2)+(-2t(2) - 2t + 2)x+(2t(5) - 6t(3) + 4t)y - t(8) + 4t(6) - 4t(4) + 2t(3) + t(2) - 2t - 0 over Z and also over finite fields F-p for primes p >= 2. Also we derive some recurrence relations on the integer solutions (x(n), y(n)) of D and formulate the the n-th solution (x(n), y(n)) by using the simple continued fraction expansion of x(n)/y(n).