1.4 KiB
1.4 KiB
id | challengeType | title |
---|---|---|
5900f4cb1000cf542c50ffdd | 5 | Problem 350: Constraining the least greatest and the greatest least |
Description
The greatest common divisor, or gcd, of a list is the largest natural number that divides all entries of the list. Examples: gcd(2,6,4) = 2, gcd(10,6,15,6) = 1 and gcd(11) = 11.
The least common multiple, or lcm, of a list is the smallest natural number divisible by each entry of the list. Examples: lcm(2,6,4) = 12, lcm(10,6,15,6) = 30 and lcm(11) = 11.
Let f(G, L, N) be the number of lists of size N with gcd ≥ G and lcm ≤ L. For example:
f(10, 100, 1) = 91. f(10, 100, 2) = 327. f(10, 100, 3) = 1135. f(10, 100, 1000) mod 1014 = 3286053.
Find f(106, 1012, 1018) mod 1014.
Instructions
Tests
tests:
- text: <code>euler350()</code> should return 84664213.
testString: assert.strictEqual(euler350(), 84664213, '<code>euler350()</code> should return 84664213.');
Challenge Seed
function euler350() {
// Good luck!
return true;
}
euler350();
Solution
// solution required