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Baltic Way
2009 Baltic Way
10
10
Part of
2009 Baltic Way
Problems
(1)
Expression with d(n)
Source: Baltic Way 2009
11/27/2010
Let
d
(
k
)
d(k)
d
(
k
)
denote the number of positive divisors of a positive integer
k
k
k
. Prove that there exist in finitely many positive integers
M
M
M
that cannot be written as
M
=
(
2
n
d
(
n
)
)
2
M=\left(\frac{2\sqrt{n}}{d(n)}\right)^2
M
=
(
d
(
n
)
2
n
)
2
for any positive integer
n
n
n
.
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number theory