## Interesting recurrence

Suppose that is a sequence of integers such that for all positive integers . Prove that for all .

**Hint** Try a combinatorial approach. Note that is uniquely defined, and can be taken as the number of binary sequences of length .

For more details see this question on Math SE

Or you can try it by induction. First note that and for prime we have . Then work with more factors inductively.

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Categories: Combinatorics, IMO, Olympiad, Problem Solving
Combinatorics, IMO, TST

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