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6
2022 Algebra/NT #6
2022 Algebra/NT #6
Source:
March 11, 2022
number theory
Problem Statement
Let f be a function from
{
1
,
2
,
.
.
.
,
22
}
\{1, 2, . . . , 22\}
{
1
,
2
,
...
,
22
}
to the positive integers such that
m
n
∣
f
(
m
)
+
f
(
n
)
mn | f(m) + f(n)
mn
∣
f
(
m
)
+
f
(
n
)
for all
m
,
n
∈
{
1
,
2
,
.
.
.
,
22
}
m, n \in \{1, 2, . . . , 22\}
m
,
n
∈
{
1
,
2
,
...
,
22
}
. If
d
d
d
is the number of positive divisors of
f
(
20
)
f(20)
f
(
20
)
, compute the minimum possible value of
d
d
d
.
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