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Simple Fractions Symmetry

Problem

Given that k and n are positive integers, and kless thann, we shall call k/n a simple fraction if it cannot be cancelled.

For example, when n=9, there are exactly six simple fractions:

1/92/94/95/97/98/9

For a given denominator, ngreater than2, prove there will always be an even number of simple fractions.

Problem ID: 166 (Apr 2004)     Difficulty: 2 Star

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