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International Contests
Nordic
1998 Nordic
4
4
Part of
1998 Nordic
Problems
(1)
when binomial is odd then we have a power of 2
Source: Nordic Mathematical Contest 1998 #4
10/3/2017
Let
n
n
n
be a positive integer. Count the number of numbers
k
∈
{
0
,
1
,
2
,
.
.
.
,
n
}
k \in \{0, 1, 2, . . . , n\}
k
∈
{
0
,
1
,
2
,
...
,
n
}
such that
(
n
k
)
\binom{n}{k}
(
k
n
)
is odd. Show that this number is a power of two, i.e. of the form
2
p
2^p
2
p
for some nonnegative integer
p
p
p
.
combinatorics
binomial coefficients
modular arithmetic