IMO Shortlist 2001 problem N1
Dodao/la:
arhiva2. travnja 2012. Prove that there is no positive integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
such that, for
![k = 1,2,\ldots,9](/media/m/5/0/e/50e7b41c3e0c62cb1a8d788c08619f5b.png)
, the leftmost digit (in decimal notation) of
![(n+k)!](/media/m/f/0/7/f074f2df0ed3b73ebd9de9e9b344bdde.png)
equals
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
.
%V0
Prove that there is no positive integer $n$ such that, for $k = 1,2,\ldots,9$, the leftmost digit (in decimal notation) of $(n+k)!$ equals $k$.
Izvor: Međunarodna matematička olimpijada, shortlist 2001