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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
27
27
Part of
PEN A Problems
Problems
(1)
A 27
Source:
5/25/2007
Show that the coefficients of a binomial expansion
(
a
+
b
)
n
(a+b)^n
(
a
+
b
)
n
where
n
n
n
is a positive integer, are all odd, if and only if
n
n
n
is of the form
2
k
ā
1
2^{k}-1
2
k
ā
1
for some positive integer
k
k
k
.
modular arithmetic
binomial coefficients
Divisibility Theory