A polynomial modulo the square of a prime

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).

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