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Prove that d_n is aperiodic

Source:

9/9/2010
Let dnd_n be the last nonzero digit of the decimal representation of n!n!. Prove that dnd_n is aperiodic; that is, there do not exist TT and n0n_0 such that for all n≥n0,dn+T=dn.n \geq n_0, d_{n+T} = d_n.
number theoryDigitdecimal representationPeriodic sequencenon-periodical functionsIMO Shortlist