Some fundamental Fibonacci number congruences

This paper investigates a number of congruence properties related to the coefficients of a generalized Fibonacci polynomial. This polynomial was defined to produce properties comparable with those of the standard polynomials of some special functions. Some of these properties are compared with known identities, while others are seemingly characteristic of arbitrary order recurrences. These include generalizations of, and analogies for, results of Appell, Bernoulli, Euler, Hilton, Horadam and Williams. In turn, the theorems lead to conjectures for further development.