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Resilience

Problem 243

Published on Saturday, 2nd May 2009, 10:00 am; Solved by 5005

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 .