## Simple Fractions Symmetry

#### Problem

Given that `k` and `n` are positive integers, and `k``n`, 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, `n`2, prove there will always be an even number of simple fractions.

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