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Putnam
1991 Putnam
B4
B4
Part of
1991 Putnam
Problems
(1)
binomial sum congruence
Source: Putnam 1991 B4
8/21/2021
Let
p
>
2
p>2
p
>
2
be a prime. Prove that
∑
n
=
0
p
(
p
n
)
(
p
+
n
n
)
≡
2
p
+
1
(
m
o
d
p
2
)
\sum_{n=0}^p\binom pn\binom{p+n}n\equiv2p+1\pmod{p^2}
∑
n
=
0
p
(
n
p
)
(
n
p
+
n
)
≡
2
p
+
1
(
mod
p
2
)
.
number theory