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IMO Shortlist
2019 IMO Shortlist
N4
Another NT FE
Another NT FE
Source: ISL 2019 N4
September 22, 2020
number theory
IMO Shortlist
IMO Shortlist 2019
functional equation
Problem Statement
Find all functions
f
:
Z
>
0
→
Z
>
0
f:\mathbb Z_{>0}\to \mathbb Z_{>0}
f
:
Z
>
0
→
Z
>
0
such that
a
+
f
(
b
)
a+f(b)
a
+
f
(
b
)
divides
a
2
+
b
f
(
a
)
a^2+bf(a)
a
2
+
b
f
(
a
)
for all positive integers
a
a
a
and
b
b
b
with
a
+
b
>
2019
a+b>2019
a
+
b
>
2019
.
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