2014 OIM Problems/Problem 6
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[hide]Problem
Given a set and a function , we say that for each , , and for each , . We say that is a fixed point of if . For each real number , we define as the number of smaller positive primes less or equal to . Given a positive integer , we say that it's "catracha" if for all Prove:
1. If is catracha, then has at least fixed points
2. If , there exist a catracha function with exactly fixed points
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
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Side note
"Catracha" is a fried tortilla, covered in fried beans and grated cheese, originating from Honduras.