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Putnam
1972 Putnam
A1
Putnam 1972 A1
Putnam 1972 A1
Source: Putnam 1972
February 17, 2022
Putnam
arithmetic sequence
binomial coefficients
Problem Statement
Show that
(
n
m
)
,
(
n
m
+
1
)
,
(
n
m
+
2
)
\binom{n}{m},\binom{n}{m+1},\binom{n}{m+2}
(
m
n
)
,
(
m
+
1
n
)
,
(
m
+
2
n
)
and
(
n
m
+
3
)
\binom{n}{m+3}
(
m
+
3
n
)
cannot be in arithmetic progression, where
n
,
m
>
0
n,m>0
n
,
m
>
0
and
n
≥
m
+
3
n\geq m+3
n
≥
m
+
3
.
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