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Putnam
1983 Putnam
A4
A4
Part of
1983 Putnam
Problems
(1)
combinatorial sum is never zero
Source: Putnam 1983 A4
9/14/2021
Let
k
k
k
be a positive integer and let
m
=
6
k
−
1
m=6k-1
m
=
6
k
−
1
. Let
S
(
m
)
=
∑
j
=
1
2
k
−
1
(
−
1
)
j
+
1
(
m
3
j
−
1
)
.
S(m)=\sum_{j=1}^{2k-1}(-1)^{j+1}\binom m{3j-1}.
S
(
m
)
=
j
=
1
∑
2
k
−
1
(
−
1
)
j
+
1
(
3
j
−
1
m
)
.
Prove that
S
(
m
)
S(m)
S
(
m
)
is never zero.
algebra