can some one tell me how to calculate a^F mod m (pow(a,F)%m), where F can be as large as Fibonacci(10^9) and m need not be a prime.( i know how to calculate the above if m is prime).Any reference is appreciated.

i know the method that you have used (ideone.com), but the problem is i may not know F but i know how to compute F (e.g F is Fibonacci(n) and n is variable, 1<n<10^9). in such cases how can i calculate the value. (in the e.g computing F doesn’t help). i need this to solve http://www.spoj.com/problems/BFALG/

I’ll look at the question as early as possible, however by your description, it seems, it can be solved by breaking it up into its prime factors and their powers.