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Putnam
1977 Putnam
A5
Putnam 1977 A5
Putnam 1977 A5
Source:
April 7, 2022
college contests
Problem Statement
Prove that
(
p
a
p
b
)
=
(
a
b
)
(
mod
p
)
\binom{pa}{pb}=\binom{a}{b} (\text{mod } p)
(
p
b
p
a
)
=
(
b
a
)
(
mod
p
)
for all integers
p
,
a
,
p,a,
p
,
a
,
and
b
b
b
with
p
p
p
a prime,
p
>
0
,
p>0,
p
>
0
,
and
a
>
b
>
0.
a>b>0.
a
>
b
>
0.
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