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A2
2011 PUMaC Algebra A2
2011 PUMaC Algebra A2
Source:
September 24, 2019
algebra
Problem Statement
A function
S
(
m
,
n
)
S(m, n)
S
(
m
,
n
)
satisfies the initial conditions
S
(
1
,
n
)
=
n
S(1, n) = n
S
(
1
,
n
)
=
n
,
S
(
m
,
1
)
=
1
S(m, 1) = 1
S
(
m
,
1
)
=
1
, and the recurrence
S
(
m
,
n
)
=
S
(
m
−
1
,
n
)
S
(
m
,
n
−
1
)
S(m, n) = S(m - 1, n)S(m, n - 1)
S
(
m
,
n
)
=
S
(
m
−
1
,
n
)
S
(
m
,
n
−
1
)
for
m
≥
2
,
n
≥
2
m\geq 2, n\geq 2
m
≥
2
,
n
≥
2
. Find the largest integer
k
k
k
such that
2
k
2^k
2
k
divides
S
(
7
,
7
)
S(7, 7)
S
(
7
,
7
)
.
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