SOLUTIONS OF SOME DIOPHANTINE EQUATIONS IN TERMS OF HORADAM SEQUENCE

Abstract

Let a, b, and P be integers such that (a, b) not equal (0, 0). In this study, we give all solutions of the equations x(2) - Pxy - y(2) = +/- (b(2) - Pab - a(2)), x(2) - (P-2 + 4)y(2) = +/- 4(b(2) - Pab - a(2)), x(2) - (P-2 +4) y(2 )= +/- 4(b(2) - Pab - a(2))(2), x(2)- Pxy + y(2) = b(2) - Pab + a(2), x(2) - (P-2 - 4)y(2) = 4(b(2) - Pab + a(2)), and x(2) - (P-2 - 4)y(2) = 4(b(2) - Pab + a(2))(2) in terms of the second order recurrence sequences when vertical bar b(2) - Pab +/- a(2)vertical bar is odd prime.