Generalised Binomial coefficients and Jarden's Theorem

We prove a stronger version of Jarden's Theorem for recurrence of powers of recursive functionsComment: A section (section 3) concerning the application of Jarden's Theorem is include

Galois Identities of the three term recurrence

We study the existence of the identity L_n^2 -5F_n^2 = 4(-1)^n