1994 OIM Problems/Problem 5
Problem
Let 
and 
be two positive integers. We wish to construct subsets 
of 
each of them with exactly 
elements and such that, for each integer 
, 
, there exist 
in 
, 
in 
, 
, 
in 
(one element in each set) with
![\[x = x_1+x_2+ \cdots +x_r\]](http://latex.artofproblemsolving.com/c/1/6/c1684f7101c5c4274f37f327593deaa16724981b.png)
Find the smallest possible value of as a function of and .
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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