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1997 USAMO
3
3
Part of
1997 USAMO
Problems
(1)
Polynomial
Source: USAMO 1997
10/9/2005
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
.
algebra
polynomial
USAMO
algorithm