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2013 IMO Shortlist
N6
N6
Part of
2013 IMO Shortlist
Problems
(1)
IMO Shortlist 2013, Number Theory #6
Source: IMO Shortlist 2013, Number Theory #6
7/10/2014
Determine all functions
f
:
Q
→
Z
f: \mathbb{Q} \rightarrow \mathbb{Z}
f
:
Q
→
Z
satisfying
f
(
f
(
x
)
+
a
b
)
=
f
(
x
+
a
b
)
f \left( \frac{f(x)+a} {b}\right) = f \left( \frac{x+a}{b} \right)
f
(
b
f
(
x
)
+
a
)
=
f
(
b
x
+
a
)
for all
x
∈
Q
x \in \mathbb{Q}
x
∈
Q
,
a
∈
Z
a \in \mathbb{Z}
a
∈
Z
, and
b
∈
Z
>
0
b \in \mathbb{Z}_{>0}
b
∈
Z
>
0
. (Here,
Z
>
0
\mathbb{Z}_{>0}
Z
>
0
denotes the set of positive integers.)
function
number theory
functional equation
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