## Modulo Summations

### Problem 326

Published on Saturday, 26th February 2011, 04:00 pm; Solved by 333; Difficulty rating: 55%
Let `a _{n}` be a sequence recursively defined by: .

So the first 10 elements of `a _{n}` are: 1,1,0,3,0,3,5,4,1,9.

Let `f`(`N,M`) represent the number of pairs (`p,q`) such that:

It can be seen that `f`(10,10)=4 with the pairs (3,3), (5,5), (7,9) and (9,10).

You are also given that `f`(10^{4},10^{3})=97158.

Find `f`(10^{12},10^{6}).