1996 OIM Problems/Problem 4

Problem

Given a natural number $n \ge 2$ , consider all fractions of the form $\frac{1}{ab}$ , where $a$ and $b$ are natural numbers, prime to each other and such that

$a < b \le n$

$a + b > n$

Prove that for each $n$ the sum of these fractions is 1/2.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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1996 OIM Problems/Problem 4

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