Difference between revisions of "2014 OIM Problems/Problem 6"
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2. If <math>n\ge36</math>, there exist a ''catracha'' function with exactly <math>\pi (x)-\pi (\sqrt{x})+1</math> fixed points | 2. If <math>n\ge36</math>, there exist a ''catracha'' function with exactly <math>\pi (x)-\pi (\sqrt{x})+1</math> fixed points | ||
+ | |||
+ | Fun fact irrelevant to the problem: ''Catracha' is a fried tortilla, covered in fried beans and grated cheese, originating from Honduras. | ||
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com |
Revision as of 15:22, 14 December 2023
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
Fun fact irrelevant to the problem: Catracha' is a fried tortilla, covered in fried beans and grated cheese, originating from Honduras.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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