53 lines
1.1 KiB
Markdown
53 lines
1.1 KiB
Markdown
---
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id: 5900f4521000cf542c50ff64
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title: 'Problem 229: Four Representations using Squares'
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challengeType: 5
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forumTopicId: 301872
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dashedName: problem-229-four-representations-using-squares
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---
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# --description--
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Consider the number 3600. It is very special, because
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3600 = 482 + 362 3600 = 202 + 2×402 3600 = 302 + 3×302 3600 = 452 + 7×152
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Similarly, we find that 88201 = 992 + 2802 = 2872 + 2×542 = 2832 + 3×522 = 1972 + 7×842.
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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:
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n = a12 + b12n = a22 + 2 b22n = a32 + 3 b32n = a72 + 7 b72,
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where the ak and bk are positive integers.
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There are 75373 such numbers that do not exceed 107.
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How many such numbers are there that do not exceed 2×109?
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# --hints--
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`euler229()` should return 11325263.
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```js
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assert.strictEqual(euler229(), 11325263);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler229() {
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return true;
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}
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euler229();
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```
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# --solutions--
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```js
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// solution required
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```
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