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USAMO
1997 USAMO
3
Polynomial
Polynomial
Source: USAMO 1997
October 9, 2005
algebra
polynomial
USAMO
algorithm
Problem Statement
Prove that for any integer
n
n
n
, there exists a unique polynomial
Q
Q
Q
with coefficients in
{
0
,
1
,
…
,
9
}
\{0,1,\ldots,9\}
{
0
,
1
,
…
,
9
}
such that
Q
(
−
2
)
=
Q
(
−
5
)
=
n
Q(-2) = Q(-5) = n
Q
(
−
2
)
=
Q
(
−
5
)
=
n
.
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