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

## Description
<section id='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).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler457()</code> should return 2647787126797397000.
    testString: assert.strictEqual(euler457(), 2647787126797397000, '<code>euler457()</code> should return 2647787126797397000.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler457() {
  // Good luck!
  return true;
}

euler457();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>