Find the number of functions f:N→N having the property that f(f(f(n)))=n+3, for any natural numbers n.
Here's an infinite family of solutions using the floor function [.]
f(n) = [n+1+a]
with a on [0,1)
Note: f(f(f(n)))=n+3 if and only if n is an integer.
https://www.desmos.com/calculator/fjxe3gnoww
Also: I don't know how to restrict the domain of a function to integers.
Edit:
One way is to make a table
https://www.desmos.com/calculator/ftlgkesfsd
Edited on February 5, 2021, 10:27 am
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Posted by Jer
on 2021-02-05 10:04:03 |
A family