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VTRMC
2017 VTRMC
6
2017 VTRMC #6
2017 VTRMC #6
Source:
August 8, 2018
Problem Statement
Let
f
(
x
)
∈
Z
[
x
]
f ( x ) \in \mathbb { Z } [ x ]
f
(
x
)
∈
Z
[
x
]
be a polynomial with integer coefficients such that
f
(
1
)
=
−
1
,
f
(
4
)
=
2
f ( 1 ) = - 1 , f ( 4 ) = 2
f
(
1
)
=
−
1
,
f
(
4
)
=
2
and
f
(
8
)
=
34
f ( 8 ) = 34
f
(
8
)
=
34
. Suppose
n
∈
Z
n\in\mathbb{Z}
n
∈
Z
is an integer such that
f
(
n
)
=
n
2
−
4
n
−
18
f ( n ) = n ^ { 2 } - 4 n - 18
f
(
n
)
=
n
2
−
4
n
−
18
. Determine all possible values for
n
n
n
.
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