MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
22
A 22
A 22
Source:
May 25, 2007
algebra
polynomial
binomial theorem
Divisibility Theory
Problem Statement
Prove that the number
∑
k
=
0
n
(
2
n
+
1
2
k
+
1
)
2
3
k
\sum_{k=0}^{n}\binom{2n+1}{2k+1}2^{3k}
k
=
0
∑
n
(
2
k
+
1
2
n
+
1
)
2
3
k
is not divisible by
5
5
5
for any integer
n
≥
0
n\geq 0
n
≥
0
.
Back to Problems
View on AoPS