ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
53 lines
1.1 KiB
Markdown
53 lines
1.1 KiB
Markdown
---
|
||
id: 5900f4521000cf542c50ff64
|
||
title: 'Problem 229: Four Representations using Squares'
|
||
challengeType: 5
|
||
forumTopicId: 301872
|
||
dashedName: problem-229-four-representations-using-squares
|
||
---
|
||
|
||
# --description--
|
||
|
||
Consider the number 3600. It is very special, because
|
||
|
||
3600 = 482 + 362 3600 = 202 + 2×402 3600 = 302 + 3×302 3600 = 452 + 7×152
|
||
|
||
Similarly, we find that 88201 = 992 + 2802 = 2872 + 2×542 = 2832 + 3×522 = 1972 + 7×842.
|
||
|
||
In 1747, Euler proved which numbers are representable as a sum of two squares. We are interested in the numbers n which admit representations of all of the following four types:
|
||
|
||
n = a12 + b12n = a22 + 2 b22n = a32 + 3 b32n = a72 + 7 b72,
|
||
|
||
where the ak and bk are positive integers.
|
||
|
||
There are 75373 such numbers that do not exceed 107.
|
||
|
||
How many such numbers are there that do not exceed 2×109?
|
||
|
||
# --hints--
|
||
|
||
`euler229()` should return 11325263.
|
||
|
||
```js
|
||
assert.strictEqual(euler229(), 11325263);
|
||
```
|
||
|
||
# --seed--
|
||
|
||
## --seed-contents--
|
||
|
||
```js
|
||
function euler229() {
|
||
|
||
return true;
|
||
}
|
||
|
||
euler229();
|
||
```
|
||
|
||
# --solutions--
|
||
|
||
```js
|
||
// solution required
|
||
```
|