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A polynomial modulo the square of a prime

Problem 457

Published on Sunday, 2nd February 2014, 04:00 am; Solved by 425; Difficulty rating: 35%

Let f(n) = n2 - 3n - 1.
Let p be a prime.
Let R(p) be the smallest positive integer n such that f(n) mod p2 = 0 if such an integer n exists, otherwise R(p) = 0.

Let SR(L) be ∑R(p) for all primes not exceeding L.

Find SR(107).