6cfd0fc503
* fix: improve Project Euler descriptions and test case Improve formatting of Project Euler test descriptions. Also add poker hands array and new test case for problem 54 * feat: add typeof tests and gave functions proper names for first 100 challenges * fix: continue fixing test descriptions and adding "before test" sections * fix: address review comments * fix: adjust grids in 18 and 67 and fix some text that reference files rather than the given arrays * fix: implement bug fixes and improvements from review * fix: remove console.log statements from seed and solution
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1.5 KiB
id, challengeType, title, forumTopicId
| id | challengeType | title | forumTopicId |
|---|---|---|---|
| 5900f3b21000cf542c50fec5 | 5 | Problem 70: Totient permutation | 302183 |
Description
Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6. The number 1 is considered to be relatively prime to every positive number, so φ(1)=1.
Interestingly, φ(87109)=79180, and it can be seen that 87109 is a permutation of 79180.
Find the value of n, 1 < n < 107, for which φ(n) is a permutation of n and the ratio n/φ(n) produces a minimum.
Instructions
Tests
tests:
- text: <code>totientPermutation()</code> should return a number.
testString: assert(typeof totientPermutation() === 'number');
- text: <code>totientPermutation()</code> should return 8319823.
testString: assert.strictEqual(totientPermutation(), 8319823);
Challenge Seed
function totientPermutation() {
// Good luck!
return true;
}
totientPermutation();
Solution
// solution required