An enormous factorial
Problem 288Published on Saturday, 17th April 2010, 01:00 pm; Solved by 1025; Difficulty rating: 30%
For any prime p the number N(p,q) is defined by
N(p,q) = ∑n=0 to q Tn*pn
with Tn generated by the following random number generator:
S0 = 290797
Sn+1 = Sn2 mod 50515093
Tn = Sn mod p
Let Nfac(p,q) be the factorial of N(p,q).
Let NF(p,q) be the number of factors p in Nfac(p,q).
You are given that NF(3,10000) mod 320=624955285.
Find NF(61,107) mod 6110