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

Source:

June 23, 2019
number theoryrelatively prime

Problem Statement

Given natural nn. Consider all the fractions 1/(pq)1/(pq), where pp and qq are relatively prime, 0<p<q≤n,p+q>n0<p<q\le n , p+q>n. Prove that the sum of all such a fractions equals to 1/21/2.
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