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2012 PUMaC Number Theory A5

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October 5, 2019
number theory

Problem Statement

Call a positive integer xx a leader if there exists a positive integer nn such that the decimal representation of xnx^n starts (not ends) with 20122012. For example, 586586 is a leader since 5863=201230056586^3 =201230056. How many leaders are there in the set {1,2,3,...,2012}\{1, 2, 3, ..., 2012\}?
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