c18554dd44
* fix: clean-up Project Euler 341-360 * fix: improve wording Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
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id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f4cb1000cf542c50ffdd | Problem 350: Constraining the least greatest and the greatest least | 5 | 302010 | problem-350-constraining-the-least-greatest-and-the-greatest-least |
--description--
A list of size n is a sequence of n natural numbers. Examples are (2, 4, 6), (2, 6, 4), (10, 6, 15, 6), and (11).
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:
$$\begin{align} & f(10, 100, 1) = 91 \\ & f(10, 100, 2) = 327 \\ & f(10, 100, 3) = 1135 \\ & f(10, 100, 1000)\bmod {101}^4 = 3\,286\,053 \end{align}$$
Find f({10}^6, {10}^{12}, {10}^{18})\bmod {101}^4.
--hints--
leastGreatestAndGreatestLeast() should return 84664213.
assert.strictEqual(leastGreatestAndGreatestLeast(), 84664213);
--seed--
--seed-contents--
function leastGreatestAndGreatestLeast() {
return true;
}
leastGreatestAndGreatestLeast();
--solutions--
// solution required