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Baltic Way
2019 Baltic Way
20
20
Part of
2019 Baltic Way
Problems
(1)
Integer polynomial with three fixed values
Source: 2019 Baltic Way P20
11/18/2019
Let us consider a polynomial
P
(
x
)
P(x)
P
(
x
)
with integers coefficients satisfying
P
(
−
1
)
=
−
4
,
P
(
−
3
)
=
−
40
,
and
P
(
−
5
)
=
−
156.
P(-1)=-4,\ P(-3)=-40,\text{ and } P(-5)=-156.
P
(
−
1
)
=
−
4
,
P
(
−
3
)
=
−
40
,
and
P
(
−
5
)
=
−
156.
What is the largest possible number of integers
x
x
x
satisfying
P
(
P
(
x
)
)
=
x
2
?
P(P(x))=x^2?
P
(
P
(
x
))
=
x
2
?
polynomial
number theory