457 - A Polynomial Modulo the Square of a Prime

Problem 457: A Polynomial Modulo the Square of a Prime

Let $f(n) = n^2 - 3n - 1$.
Let $p$ be a prime.
Let $R(p)$ be the smallest positive integer $n$ such that $f(n) \bmod p^2 = 0$ if such an integer $n$ exists, otherwise $R(p) = 0$.

Let $SR(L)$ be $\sum R(p)$ for all primes not exceeding $L$.

Find $SR(10^7)$.