76 lines
1.3 KiB
Markdown
76 lines
1.3 KiB
Markdown
---
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id: 5900f4521000cf542c50ff64
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challengeType: 5
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title: 'Problem 229: Four Representations using Squares'
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forumTopicId: 301872
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---
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## Description
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<section id='description'>
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Consider the number 3600. It is very special, because
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3600 = 482 + 362
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3600 = 202 + 2×402
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3600 = 302 + 3×302
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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.
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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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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler229()</code> should return 11325263.
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testString: assert.strictEqual(euler229(), 11325263);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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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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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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