This paper shows that every uniform power function of power p of Fibonacci and Lucas numbers can be expressed alternatively both as  and as  The proof also includes the proof of R. S. Melham’s conjectures on certain classes of Fibonacci identities. Formulae and algorithms for the calculation of coefficients for such identities are set forth. The analysis is then expanded to apply to recurrence sequences in the form

Fibonacci, Lucas, identity, uniform power, primitive identity, congruent identity, generalized recurrence sequence, Melham’s conjecture, uniform power function, uniform power sum, uniform power identity, UPI, Lucasian twin, base sequence, Lucas sequence, Hyper-Lucas sequence.