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Contests
National and Regional Contests
PEN Problems
PEN Q Problems
1
1
Part of
PEN Q Problems
Problems
(1)
Q 1
Source:
5/25/2007
Suppose
p
(
x
)
∈
Z
[
x
]
p(x) \in \mathbb{Z}[x]
p
(
x
)
∈
Z
[
x
]
and
P
(
a
)
P
(
b
)
=
−
(
a
−
b
)
2
P(a)P(b)=-(a-b)^2
P
(
a
)
P
(
b
)
=
−
(
a
−
b
)
2
for some distinct
a
,
b
∈
Z
a, b \in \mathbb{Z}
a
,
b
∈
Z
. Prove that
P
(
a
)
+
P
(
b
)
=
0
P(a)+P(b)=0
P
(
a
)
+
P
(
b
)
=
0
.
Polynomials