Let S be the smallest set of positive integers such that
a) 2 is in S,
b) n is in S whenever n^2 is in S, and
c) (n + 5)^2 is in S whenever n is in S.
Which positive integers are not in S?

(The set S is “smallest” in the sense that S is contained in any other such set.)

Source: Putnam 2017

(In reply to flawed program, but some ideas by Charlie)

If after a certain point every number ending in 9 is on the list (certainly 49, 59, ...) that will include every square of numbers ending in 3 and therefore every number ending in 3 after that point should be on the list (members of S); for example 169 should be on the list and it follows that 13 is on it.

Posted by Charlie on 2024-02-18 10:32:33