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National and Regional Contests
PEN Problems
PEN K Problems
11
11
Part of
PEN K Problems
Problems
(1)
K 11
Source:
5/25/2007
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
m
,
n
∈
N
0
m,n\in \mathbb{N}_{0}
m
,
n
∈
N
0
:
m
f
(
n
)
+
n
f
(
m
)
=
(
m
+
n
)
f
(
m
2
+
n
2
)
.
mf(n)+nf(m)=(m+n)f(m^{2}+n^{2}).
m
f
(
n
)
+
n
f
(
m
)
=
(
m
+
n
)
f
(
m
2
+
n
2
)
.
function
algebra
functional equation
Functional Equations