49 lines
1.0 KiB
Markdown
49 lines
1.0 KiB
Markdown
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---
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id: 5900f43c1000cf542c50ff4e
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title: 'Problem 207: Integer partition equations'
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challengeType: 5
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forumTopicId: 301848
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dashedName: problem-207-integer-partition-equations
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---
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# --description--
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For some positive integers k, there exists an integer partition of the form 4t = 2t + k,
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where 4t, 2t, and k are all positive integers and t is a real number.
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The first two such partitions are 41 = 21 + 2 and 41.5849625... = 21.5849625... + 6.
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Partitions where t is also an integer are called perfect. For any m ≥ 1 let P(m) be the proportion of such partitions that are perfect with k ≤ m. Thus P(6) = 1/2.
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In the following table are listed some values of P(m) P(5) = 1/1 P(10) = 1/2 P(15) = 2/3 P(20) = 1/2 P(25) = 1/2 P(30) = 2/5 ... P(180) = 1/4 P(185) = 3/13
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Find the smallest m for which P(m) < 1/12345
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# --hints--
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`euler207()` should return 44043947822.
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```js
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assert.strictEqual(euler207(), 44043947822);
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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 euler207() {
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return true;
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}
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euler207();
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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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