2002 AIME I Problems/Problem 9
Problem
Harold, Tanya, and Ulysses paint a very long picket fence.
Harold starts with the first picket and paints every 
th picket;
Tanya starts with the second picket and paints every 
th picket; and
Ulysses starts with the third picket and paints every 
th picket.
Call the positive integer 
paintable when the triple 
of positive integers results in every picket being painted exaclty once. Find the sum of all the paintable integers.
Solution
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