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Apr 14, 2016 at 1:01 history edited Douglas Zare CC BY-SA 3.0
Corrected definition of base factorial.
Apr 14, 2016 at 1:00 comment added Douglas Zare @Tony Huynh: Yes, thanks, I'll correct that.
Apr 13, 2016 at 21:23 comment added Tony Huynh I think you want $n_i \leq i$ instead of $n_i < i$. A slightly easier argument is to observe that $a_i!$ can occur at most $a_i$ times in any optimal representation for $n$ with the minimal number of terms. The rest follows since the base factorial representation of a number is unique.
Apr 13, 2016 at 20:47 vote accept CommunityBot
Apr 13, 2016 at 17:07 history answered Douglas Zare CC BY-SA 3.0