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Laurențiu Panaitopol, Tulcea
2010 Laurențiu Panaitopol, Tulcea
3
A nice problem with polynoms by Panaitopol
A nice problem with polynoms by Panaitopol
Source:
October 28, 2019
polynoms
algebra
Problem Statement
Let be two polynoms
P
,
Q
∈
R
[
X
]
P,Q\in\mathbb{R} [X]
P
,
Q
∈
R
[
X
]
having the property that
∣
{
n
∈
{
0
}
∪
N
∣
P
(
n
)
≤
Q
(
n
)
}
∣
=
∣
{
n
∈
{
0
}
∪
N
∣
P
(
n
)
≥
Q
(
n
)
}
∣
=
∞
.
\left| \{ n\in\{ 0\}\cup\mathbb{N} | P(n)\le Q(n) \} \right| =\left| \{ n\in\{ 0\}\cup\mathbb{N} | P(n)\ge Q(n) \} \right| =\infty .
∣
{
n
∈
{
0
}
∪
N
∣
P
(
n
)
≤
Q
(
n
)}
∣
=
∣
{
n
∈
{
0
}
∪
N
∣
P
(
n
)
≥
Q
(
n
)}
∣
=
∞.
Show that
P
=
Q
.
P=Q.
P
=
Q
.
Laurențiu Panaitopol
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