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2018 IMO Shortlist
N6
N6
Part of
2018 IMO Shortlist
Problems
(1)
Unique NT Function
Source: IMO SL 2018 N6
7/17/2019
Let
f
:
{
1
,
2
,
3
,
…
}
→
{
2
,
3
,
…
}
f : \{ 1, 2, 3, \dots \} \to \{ 2, 3, \dots \}
f
:
{
1
,
2
,
3
,
…
}
→
{
2
,
3
,
…
}
be a function such that
f
(
m
+
n
)
∣
f
(
m
)
+
f
(
n
)
f(m + n) | f(m) + f(n)
f
(
m
+
n
)
∣
f
(
m
)
+
f
(
n
)
for all pairs
m
,
n
m,n
m
,
n
of positive integers. Prove that there exists a positive integer
c
>
1
c > 1
c
>
1
which divides all values of
f
f
f
.
function
number theory
IMO Shortlist