IMO Shortlist 1983 problem 24
Dodao/la:
arhiva2. travnja 2012. Let
![d_n](/media/m/f/b/c/fbc5ddc25333c65de698bb0b30645cfe.png)
be the last nonzero digit of the decimal representation of
![n!](/media/m/5/e/9/5e9bb819f1bfbf465700f6bc8831a1c7.png)
. Prove that
![d_n](/media/m/f/b/c/fbc5ddc25333c65de698bb0b30645cfe.png)
is aperiodic; that is, there do not exist
![T](/media/m/0/1/6/016d42c58f7f5f06bdf8af6b85141914.png)
and
![n_0](/media/m/2/2/a/22a23a21b7b74b6120b58e119a1f870c.png)
such that for all
%V0
Let $d_n$ be the last nonzero digit of the decimal representation of $n!$. Prove that $d_n$ is aperiodic; that is, there do not exist $T$ and $n_0$ such that for all $n \geq n_0, d_{n+T} = d_n.$
Izvor: Međunarodna matematička olimpijada, shortlist 1983