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>
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id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f4521000cf542c50ff64 | Problem 229: Four Representations using Squares | 5 | 301872 | 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.
assert.strictEqual(euler229(), 11325263);
--seed--
--seed-contents--
function euler229() {
return true;
}
euler229();
--solutions--
// solution required