## A polynomial modulo the square of a prime

### Problem 457

Published on Sunday, 2nd February 2014, 04:00 am; Solved by 338; Difficulty rating: 35%
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 SR(`L`) be ∑R(`p`) for all primes not exceeding `L`.

Find SR(10^{7}).