MYTS 2018 - Grade 8 - Round 2 Question 6

For each integer n≥2, let F_n be the set of fractions a/b with 0≤a$<$b≤n and gcd(a,b)=1. For example F_2={0/1,1/2}, F_3={0/1,1/3,1/2,2/3}, F_4={0/1,1/4,1/3,1/2,2/3,3/4}. Prove that F_n has an even number of elements.