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Brazil National Olympiad
1988 Brazil National Olympiad
3
Product-to-sum function
Product-to-sum function
Source:
December 27, 2017
Brazilian Math Olympiad 1988
functions
number theory
Brazilian Math Olympiad
function
Problem Statement
Find all functions
f
:
N
∗
→
N
f:\mathbb{N}^* \rightarrow \mathbb{N}
f
:
N
∗
→
N
such that [*]
f
(
x
⋅
y
)
=
f
(
x
)
+
f
(
y
)
f(x \cdot y) = f(x) + f(y)
f
(
x
⋅
y
)
=
f
(
x
)
+
f
(
y
)
[*]
f
(
30
)
=
0
f(30) = 0
f
(
30
)
=
0
[*]
f
(
x
)
=
0
f(x)=0
f
(
x
)
=
0
always when the units digit of
x
x
x
is
7
7
7
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