1.2 KiB
1.2 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4601000cf542c50ff73 | Problem 243: Resilience | 5 | 301890 | problem-243-resilience |
--description--
A positive fraction whose numerator is less than its denominator is called a proper fraction.
For any denominator, d
, there will be d−1
proper fractions; for example, with d = 12
:
\frac{1}{12}, \frac{2}{12}, \frac{3}{12}, \frac{4}{12}, \frac{5}{12}, \frac{6}{12}, \frac{7}{12}, \frac{8}{12}, \frac{9}{12}, \frac{10}{12}, \frac{11}{12}
We shall call a fraction that cannot be cancelled down a resilient fraction.
Furthermore we shall define the resilience of a denominator, R(d)
, to be the ratio of its proper fractions that are resilient; for example, R(12) = \frac{4}{11}
.
In fact, d = 12
is the smallest denominator having a resilience R(d) < \frac{4}{10}
.
Find the smallest denominator d
, having a resilience R(d) < \frac{15\\,499}{94\\,744}
.
--hints--
resilience()
should return 892371480
.
assert.strictEqual(resilience(), 892371480);
--seed--
--seed-contents--
function resilience() {
return true;
}
resilience();
--solutions--
// solution required