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South Africa Contests
South Africa National Olympiad
1998 South africa National Olympiad
5
Gcd of binomial coefficients
Gcd of binomial coefficients
Source: South Africa 1998
September 30, 2005
number theory
greatest common divisor
number theory solved
Problem Statement
Prove that
gcd
(
(
n
1
)
,
(
n
2
)
,
…
,
(
n
n
−
1
)
)
\gcd{\left({n \choose 1},{n \choose 2},\dots,{n \choose {n - 1}}\right)}
g
cd
(
(
1
n
)
,
(
2
n
)
,
…
,
(
n
−
1
n
)
)
is a prime if
n
n
n
is a power of a prime, and 1 otherwise.
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