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A1

Part of 2017 Putnam

Problems(1)

Putnam 2017 A1

Source:

12/3/2017
Let SS be the smallest set of positive integers such that
a) 22 is in S,S, b) nn is in SS whenever n2n^2 is in S,S, and c) (n+5)2(n+5)^2 is in SS whenever nn is in S.S.
Which positive integers are not in S?S?
(The set SS is ``smallest" in the sense that SS is contained in any other such set.)
PutnamPutnam 2017