45 lines
761 B
Markdown
45 lines
761 B
Markdown
|
---
|
|||
|
id: 5900f3e71000cf542c50fefa
|
|||
|
title: 'Problem 123: Prime square remainders'
|
|||
|
challengeType: 5
|
|||
|
forumTopicId: 301750
|
|||
|
dashedName: problem-123-prime-square-remainders
|
|||
|
---
|
|||
|
|
|||
|
# --description--
|
|||
|
|
|||
|
Let pn be the nth prime: 2, 3, 5, 7, 11, ..., and let r be the remainder when (pn−1)n + (pn+1)n is divided by pn2.
|
|||
|
|
|||
|
For example, when n = 3, p3 = 5, and 43 + 63 = 280 ≡ 5 mod 25.
|
|||
|
|
|||
|
The least value of n for which the remainder first exceeds 109 is 7037.
|
|||
|
|
|||
|
Find the least value of n for which the remainder first exceeds 1010.
|
|||
|
|
|||
|
# --hints--
|
|||
|
|
|||
|
`euler123()` should return 21035.
|
|||
|
|
|||
|
```js
|
|||
|
assert.strictEqual(euler123(), 21035);
|
|||
|
```
|
|||
|
|
|||
|
# --seed--
|
|||
|
|
|||
|
## --seed-contents--
|
|||
|
|
|||
|
```js
|
|||
|
function euler123() {
|
|||
|
|
|||
|
return true;
|
|||
|
}
|
|||
|
|
|||
|
euler123();
|
|||
|
```
|
|||
|
|
|||
|
# --solutions--
|
|||
|
|
|||
|
```js
|
|||
|
// solution required
|
|||
|
```
|