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Contests
National and Regional Contests
Turkey Contests
Turkey Team Selection Test
2023 Turkey Team Selection Test
3
3
Part of
2023 Turkey Team Selection Test
Problems
(1)
Values of n-f(n)
Source: 2023 Turkey TST D1 P3
3/29/2023
For all
n
>
1
n>1
n
>
1
, let
f
(
n
)
f(n)
f
(
n
)
be the biggest divisor of
n
n
n
except itself. Does there exists a positive integer
k
k
k
such that the equality
n
ā
f
(
n
)
=
k
n-f(n)=k
n
ā
f
(
n
)
=
k
has exactly
2023
2023
2023
solutions?
number theory
equation