MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Polish MO Finals
1990 Polish MO Finals
3
Sum divisible by 3
Sum divisible by 3
Source: Problem 6, Polish NO 1990
September 30, 2005
modular arithmetic
number theory unsolved
number theory
Problem Statement
Prove that for all integers
n
>
2
n > 2
n
>
2
,
3
∣
∑
i
=
0
[
n
/
3
]
(
−
1
)
i
C
n
3
i
3| \sum\limits_{i=0}^{[n/3]} (-1)^i C _n ^{3i}
3∣
i
=
0
∑
[
n
/3
]
(
−
1
)
i
C
n
3
i
Back to Problems
View on AoPS