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7
SMT 2023 Discrete #7
SMT 2023 Discrete #7
Source:
May 3, 2023
Problem Statement
Let
S
S
S
be the number of bijective functions
f
:
{
0
,
1
,
…
,
288
}
→
{
0
,
1
,
…
,
288
}
f:\{0,1,\dots,288\}\rightarrow\{0,1,\dots,288\}
f
:
{
0
,
1
,
…
,
288
}
→
{
0
,
1
,
…
,
288
}
such that
f
(
(
m
+
n
)
(
m
o
d
17
)
)
f((m+n)\pmod{17})
f
((
m
+
n
)
(
mod
17
))
is divisible by
17
17
17
if and only if
f
(
m
)
+
f
(
n
)
f(m)+f(n)
f
(
m
)
+
f
(
n
)
is divisible by
17
17
17
. Compute the largest positive integer
n
n
n
such that
2
n
2^n
2
n
divides
S
S
S
.
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