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PEN K Problems
34
K 34
K 34
Source:
May 25, 2007
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Functional Equations
Problem Statement
Show that there exists a bijective function
f
:
N
0
→
N
0
f: \mathbb{N}_{0}\to \mathbb{N}_{0}
f
:
N
0
→
N
0
such that for all
m
,
n
∈
N
0
m,n\in \mathbb{N}_{0}
m
,
n
∈
N
0
:
f
(
3
m
n
+
m
+
n
)
=
4
f
(
m
)
f
(
n
)
+
f
(
m
)
+
f
(
n
)
.
f(3mn+m+n)=4f(m)f(n)+f(m)+f(n).
f
(
3
mn
+
m
+
n
)
=
4
f
(
m
)
f
(
n
)
+
f
(
m
)
+
f
(
n
)
.
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