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2013 Japan MO Finals
2
2013 Japan Mathematical Olympiad Finals Problem 2
2013 Japan Mathematical Olympiad Finals Problem 2
Source:
February 11, 2013
function
induction
algebra proposed
algebra
Problem Statement
Find all functions
f
:
Z
→
R
f:\mathbb{Z}\rightarrow\mathbb{R}
f
:
Z
→
R
such that the equality
f
(
m
)
+
f
(
n
)
=
f
(
m
n
)
+
f
(
m
+
n
+
m
n
)
f(m)+f(n)=f(mn)+f(m+n+mn)
f
(
m
)
+
f
(
n
)
=
f
(
mn
)
+
f
(
m
+
n
+
mn
)
holds for all
m
,
n
∈
Z
.
m,n\in\mathbb{Z}.
m
,
n
∈
Z
.
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