---
id: 5900f5361000cf542c510048
title: 'Problem 457: A polynomial modulo the square of a prime'
challengeType: 5
forumTopicId: 302131
dashedName: problem-457-a-polynomial-modulo-the-square-of-a-prime
---

# --description--

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).

# --hints--

`euler457()` should return 2647787126797397000.

```js
assert.strictEqual(euler457(), 2647787126797397000);
```

# --seed--

## --seed-contents--

```js
function euler457() {

  return true;
}

euler457();
```

# --solutions--

```js
// solution required
```