# 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 .