View source for 1996 OIM Problems/Problem 4

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

<cmath>a < b \le n</cmath>

<cmath>a + b > n</cmath>

Prove that for each <math>n</math> the sum of these fractions is 1/2.

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

== Solution ==
{{solution}}

== See also ==
https://www.oma.org.ar/enunciados/ibe11.htm