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2013 IMO Shortlist
N1
N1
Part of
2013 IMO Shortlist
Problems
(1)
IMO Shortlist 2013, Number Theory #1
Source: IMO Shortlist 2013, Number Theory #1
7/10/2014
Let
Z
>
0
\mathbb{Z} _{>0}
Z
>
0
be the set of positive integers. Find all functions
f
:
Z
>
0
→
Z
>
0
f: \mathbb{Z} _{>0}\rightarrow \mathbb{Z} _{>0}
f
:
Z
>
0
→
Z
>
0
such that
m
2
+
f
(
n
)
∣
m
f
(
m
)
+
n
m^2 + f(n) \mid mf(m) +n
m
2
+
f
(
n
)
∣
m
f
(
m
)
+
n
for all positive integers
m
m
m
and
n
n
n
.
number theory
algebra
functional equation
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