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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