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Moldova Contests
Moldova Team Selection Test
2005 Moldova Team Selection Test
3
n^k divides [A]
n^k divides [A]
Source: Moldova TST 2005
March 21, 2005
calculus
integration
function
number theory proposed
number theory
Problem Statement
A
=
3
∑
m
=
1
n
2
(
1
2
−
{
m
}
)
A=3\sum_{m=1}^{n^2}(\frac12-\{\sqrt{m}\})
A
=
3
m
=
1
∑
n
2
(
2
1
−
{
m
})
where
n
n
n
is an positive integer. Find the largest
k
k
k
such that
n
k
n^k
n
k
divides
[
A
]
[A]
[
A
]
.
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