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Contests
National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2022 Dutch BxMO TST
1
1
Part of
2022 Dutch BxMO TST
Problems
(1)
f(n) | f(m) - n iff n | m for all n,m
Source: 2022 Dutch BxMO TST p1
12/3/2022
Find all functions
f
:
Z
>
0
→
Z
>
0
f : Z_{>0} \to Z_{>0}
f
:
Z
>
0
→
Z
>
0
for which
f
(
n
)
∣
f
(
m
)
−
n
f(n) | f(m) - n
f
(
n
)
∣
f
(
m
)
−
n
if and only if
n
∣
m
n | m
n
∣
m
for all natural numbers
m
m
m
and
n
n
n
.
number theory
functional