Solutions of Some Diophantine Equations in terms of Generalized Fibonacci and Lucas Numbers

In this study, we present some identities involving generalized Fibonacci sequence (U-n) and generalized Lucas sequence (V-n). Then we give all solutions of the Diophantine equations x(2) -V-n(xy) vertical bar (-1)(n)y(2) - +/- (p(2) vertical bar 4)U-n(2), x(2) - V-n(xy) vertical bar (-1)(n)y(2) = +/- U-n(2), x(2) - x(2) - (p(2) vertical bar 4)U(n)xy - (p(2) + 4)(-1)(n)y(2) = +/- V-n(2), x(2) - V(n)xy +/- y(2) = +/- 1, x(2) - (p(2) +4)U(n)xy -(p(2) + 4)(-1)(n)y(2) = 1, x(2) -V(2n)xy +(-1)ny(2) - +/-(p(2) +4)V-n(2), x(2) - V(2x)y + y(2) -+/-(p(2) +4)V-n(2), x(2)-V(2n)xy + y(2) - (p(2) +4)U-n(2) and x(2) - V(2n)xy + y(2) = +/- V-n(2) in terms of the sequences (U-n) and (V-n) with p >= 21 and p2 + 4 squarefree.