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MathLinks Contest 4th
2.3
0423 combinations sum 4th edition Round 2 p3
0423 combinations sum 4th edition Round 2 p3
Source:
May 7, 2021
algebra
4th edition
Problem Statement
Let
m
≥
2
n
m \ge 2n
m
≥
2
n
be two positive integers. Find a closed form for the following expression:
E
(
m
,
n
)
=
∑
k
=
0
n
(
−
1
)
k
(
m
−
k
n
)
(
n
k
)
E(m, n) = \sum_{k=0}^{n} (-1)^k {{m- k} \choose n} { n \choose k}
E
(
m
,
n
)
=
k
=
0
∑
n
(
−
1
)
k
(
n
m
−
k
)
(
k
n
)
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