1.0 KiB
1.0 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f43c1000cf542c50ff4e | Problem 207: Integer partition equations | 5 | 301848 | problem-207-integer-partition-equations |
--description--
For some positive integers k, there exists an integer partition of the form 4t = 2t + k,
where 4t, 2t, and k are all positive integers and t is a real number.
The first two such partitions are 41 = 21 + 2 and 41.5849625... = 21.5849625... + 6.
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.
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
Find the smallest m for which P(m) < 1/12345
--hints--
euler207()
should return 44043947822.
assert.strictEqual(euler207(), 44043947822);
--seed--
--seed-contents--
function euler207() {
return true;
}
euler207();
--solutions--
// solution required