Clifford A. Reiter, Fast Fibonacci Numbers,The Mathematica Journal , 2 3 (1992) 58-60.

This paper invesigates several techniques, implemented in Mathematica, for rapidly computing very large Fibonacci numbers. Reduction formulas are described that give formulas for leaps forward by specified factors. In some circumstances, these formulas give remarkably efficient schemes for computing these large Fibonacci numbers.

See Also: · A motivating reference was: R. E. Maeder, Fibonacci on the Fast Track, The Mathematica Journal, 1 3 (1991) 42-46. · The study of the canonical forms of reduction formulas of the type used here, but applied to locating moduli where the Fibonacci sequence has short periods appears in [nt_1993]