MathDB
Problems
Contests
National and Regional Contests
China Contests
South East Mathematical Olympiad
2020 South East Mathematical Olympiad
3
3
Part of
2020 South East Mathematical Olympiad
Problems
(1)
Polynomial without negative integer roots has many positive integer roots
Source: 2020 China Southeast 10.3/11.3
8/7/2020
Given a polynomial
f
(
x
)
=
x
2020
+
∑
i
=
0
2019
c
i
x
i
f(x)=x^{2020}+\sum_{i=0}^{2019} c_ix^i
f
(
x
)
=
x
2020
+
∑
i
=
0
2019
c
i
x
i
, where
c
i
∈
{
−
1
,
0
,
1
}
c_i \in \{ -1,0,1 \}
c
i
∈
{
−
1
,
0
,
1
}
. Denote
N
N
N
the number of positive integer roots of
f
(
x
)
=
0
f(x)=0
f
(
x
)
=
0
(counting multiplicity). If
f
(
x
)
=
0
f(x)=0
f
(
x
)
=
0
has no negative integer roots, find the maximum of
N
N
N
.
algebra
polynomial