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non-periodic sequence

Source: Bundeswettbewerb Mathematik 1986, second stage, problem 3

May 14, 2004
algebra unsolvedalgebra

Problem Statement

Let dnd_n be the last digit, distinct from 0, in the decimal expansion of n!n!. Prove that the sequence d1,d2,d3,…d_1,d_2,d_3, \ldots is not periodic.
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