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National and Regional Contests
Vietnam Contests
Vietnam Team Selection Test
2014 Vietnam Team Selection Test
1
Functional equation
Functional equation
Source: Vietnam TST 2014
February 22, 2015
induction
algebra unsolved
algebra
Problem Statement
Find all
f
:
Z
→
Z
f:\mathbb{Z}\rightarrow\mathbb{Z}
f
:
Z
→
Z
such that
f
(
2
m
+
f
(
m
)
+
f
(
m
)
f
(
n
)
)
=
n
f
(
m
)
+
m
f(2m+f(m)+f(m)f(n))=nf(m)+m
f
(
2
m
+
f
(
m
)
+
f
(
m
)
f
(
n
))
=
n
f
(
m
)
+
m
∀
m
,
n
∈
Z
\forall m,n\in\mathbb{Z}
∀
m
,
n
∈
Z
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