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Kürschák Math Competition
1999 Kurschak Competition
1
1
Part of
1999 Kurschak Competition
Problems
(1)
Number of even and odd divisors
Source: Kürschák 1999, problem 1
7/15/2014
For any positive integer
m
m
m
, denote by
d
i
(
m
)
d_i(m)
d
i
(
m
)
the number of positive divisors of
m
m
m
that are congruent to
i
i
i
modulo
2
2
2
. Prove that if
n
n
n
is a positive integer, then
∣
∑
k
=
1
n
(
d
0
(
k
)
−
d
1
(
k
)
)
∣
≤
n
.
\left|\sum_{k=1}^n \left(d_0(k)-d_1(k)\right)\right|\le n.
k
=
1
∑
n
(
d
0
(
k
)
−
d
1
(
k
)
)
≤
n
.
number theory unsolved
number theory