120

Part of 1969 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 120 All Soviet Union MO 1969 sum of 1/(pq), with coprime

Source:

n

. Consider all the fractions

1/(pq)

p

q

are relatively prime,

0<p<q\le n , p+q>n

. Prove that the sum of all such a fractions equals to

1/2

number theoryrelatively prime