MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Poland - Second Round
2003 Poland - Second Round
1
1
Part of
2003 Poland - Second Round
Problems
(1)
Sequence of binomial coefficients
Source: 54 Polish MO 2003 Second Round - First Day Problem 1
4/21/2018
Prove that exists integer
n
>
2003
n > 2003
n
>
2003
that in sequence
(
n
0
)
\binom{n}{0}
(
0
n
)
,
(
n
1
)
\binom{n}{1}
(
1
n
)
,
(
n
2
)
\binom{n}{2}
(
2
n
)
, ...,
(
n
2003
)
\binom{n}{2003}
(
2003
n
)
each element is a divisor of all elements which are after him.
number theory
binomial coefficients
Poland