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MathLinks Contest 5th
2.1
0521 functional in N 5th edition Round 2 p1
0521 functional in N 5th edition Round 2 p1
Source:
May 6, 2021
functional equation
5th edition
Problem Statement
For what positive integers
k
k
k
there exists a function
f
:
N
→
N
f : N \to N
f
:
N
→
N
such that for all
n
∈
N
n \in N
n
∈
N
we have
f(f(... f(n)....))
⏟
k times
=
f
(
n
)
+
2
\underbrace{\hbox{f(f(... f(n)....))}}_{\hbox{k times}} = f(n) + 2
k times
f(f(... f(n)....))
=
f
(
n
)
+
2
?
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