1993 OIM Problems/Problem 6
Problem
Two non-negative integers 
and 
are "mates" if the decimal expression 
consists only of zeros and ones. Let 
and 
be two infinite sets of non-negative integers, such that is the set of all numbers that are "mates" of all the elements of .
Prove that in one of the sets or there are infinitely many pairs of numbers 
, and 
such that 
.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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