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PEN K Problems
10
K 10
K 10
Source:
May 25, 2007
function
induction
Functional Equations
Problem Statement
Find all functions
f
:
N
0
→
N
0
f: \mathbb{N}_{0}\to \mathbb{N}_{0}
f
:
N
0
→
N
0
such that for all
n
∈
N
0
n\in \mathbb{N}_{0}
n
∈
N
0
:
f
(
m
+
f
(
n
)
)
=
f
(
f
(
m
)
)
+
f
(
n
)
.
f(m+f(n))=f(f(m))+f(n).
f
(
m
+
f
(
n
))
=
f
(
f
(
m
))
+
f
(
n
)
.
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