USAMO 2007 Problem 1
Posted: Wed Apr 25, 2007 5:30 pmLet n be a positive integer. Define a sequence by setting [unparseable or potentially dangerous latex formula] and, for each [unparseable or potentially dangerous latex formula], letting [unparseable or potentially dangerous latex formula] be the unique integer in the range [unparseable or potentially dangerous latex formula] for which [unparseable or potentially dangerous latex formula] is divisible by [unparseable or potentially dangerous latex formula]. For instance, when [unparseable or potentially dangerous latex formula] the obtained sequence is [unparseable or potentially dangerous latex formula] Prove that for any [unparseable or potentially dangerous latex formula] the sequence [unparseable or potentially dangerous latex formula] eventually becomes constant.