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Lady and the stamps of value 5, n, and n+1

Source: 2019 AIME II #14

March 22, 2019
AMCAIMEAIME II2019 AIME II2019 AMCnumber theoryChicken McNugget Theorem

Problem Statement

Find the sum of all positive integers nn such that, given an unlimited supply of stamps of denominations 55, nn, and n+1n + 1 cents, 9191 cents is the greatest postage that cannot be formed.
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