Difference between revisions of "1996 OIM Problems/Problem 4"
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Latest revision as of 15:05, 13 December 2023
Problem
Given a natural number 
, consider all fractions of the form 
, where 
and 
are natural numbers, prime to each other and such that
![\[a < b \le n\]](http://latex.artofproblemsolving.com/f/2/4/f2482259c5da8528a4a6fa298bcb20d092ccccd2.png)
![\[a + b > n\]](http://latex.artofproblemsolving.com/b/e/6/be609c94df29401bbd2b8dab70889d61870bcecf.png)
Prove that for each 
the sum of these fractions is 1/2.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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