Problem of the Week

Take any 2 positive integers.  If neither of them is even, then they are both odd and their sum is then even.   So for each set of 2 postive integers, it is always possible to find a subset of the set whose sum is divisible by 2.

Now, take any set of 139 postive integers.  Is always possible to find a non-empty subset of this set whose sum is divisible by 139?

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ã2002 Alberto L. Delgado