IMO Shortlist 1991 problem 14
Dodao/la:
arhiva2. travnja 2012. Let
![a_n](/media/m/1/f/f/1ff6f81c68b9c6fb726845c9ce762d7a.png)
be the last nonzero digit in the decimal representation of the number
![n!.](/media/m/f/b/2/fb282ce47c039c8f6ba04e20489094a9.png)
Does the sequence
![a_1, a_2, \ldots, a_n, \ldots](/media/m/9/9/c/99c7c6a30a517fc7873f932322bffdf4.png)
become periodic after a finite number of terms?
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Let $a_n$ be the last nonzero digit in the decimal representation of the number $n!.$ Does the sequence $a_1, a_2, \ldots, a_n, \ldots$ become periodic after a finite number of terms?
Izvor: Međunarodna matematička olimpijada, shortlist 1991