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2000 Harvard-MIT Mathematics Tournament
11
2000 HMMT RMT Team #11
2000 HMMT RMT Team #11
Source:
March 8, 2024
algebra
Problem Statement
Find all polynomials
f
(
x
)
f(x)
f
(
x
)
with integer coefficients such that the coefficients of both
f
(
x
)
f(x)
f
(
x
)
and
[
f
(
x
)
]
3
[f(x)]^3
[
f
(
x
)
]
3
lie in the set
{
0
,
1
,
ā
1
}
\{0,1, -1\}
{
0
,
1
,
ā
1
}
.
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