Problem 243
Resilience
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:
1/12 , 2/12 , 3/12 , 4/12 , 5/12 , 6/12 , 7/12 , 8/12 , 9/12 , 10/12 , 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) = 4/11 .
In fact, d = 12 is the smallest denominator having a resilience R(d) < 4/10 .
Find the smallest denominator d, having a resilience R(d) < 15499/94744 .
不可约度
分子小于分母的正分数被称为真分数。
对于分母d，一共有d-1个真分数；例如，当d = 12时为：
1/12、2/12、3/12、4/12、5/12、6/12、7/12、8/12、9/12、10/12、11/12。
我们称不能被约简的分数为不可约分数。
进一步地，我们可以定义分母的不可约度R(d)为它的真分数中不可约分数的比例；例如，R(12) = 4/11。
事实上，d = 12是不可约度R(d) < 4/10的最小分母。
求不可约度R(d) < 15499/94744的最小分母d。