On some Diophantine equations

Abstract

for p >= 3 and a square-free integer p(2) - 4. In addition to these, all solutions of some different Diophantine equations such as x(2) - v(2n)xy + y(2) = -(p(2) - 4)u(n)(2), x(2) - v(n)xy + y(2) = -(p(2) - 4), x(2) - v(n)xy + y(2) = 1, x(2) - v(2n)xy + y(2) = u(n)(2), x(2) - v(2n)xy + y(2) = v(n)(2), x(2) - (p(2) - 4)u(n)xy - (p(2) - 4)y(2) = 1 are identified, by using divisibility rules of the sequences (u(n)) and (v(n)).