A Polynomial Modulo the Square of a Prime

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

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

Find $S R (10^{7})$ .

Write-up coming later

The complete problem is available here. An approach, code, and answer will be added later.