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all digits exactly once in one of numbers A, A^2, A^ 3

Source: Singapore Junior Math Olympiad 2012 2nd Round p2 SMO

March 25, 2020
Digitsnumber theory

Problem Statement

Does there exist an integer AA such that each of the ten digits 0,1,...,90, 1, . . . , 9 appears exactly once as a digit in exactly one of the numbers A,A2,A3A, A^2, A^ 3 ?
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