MathDB
Problems
Contests
National and Regional Contests
Greece Contests
Greece Junior Math Olympiad
1987 Greece Junior Math Olympiad
3
x^{n+1}+ax+b divisible by (x-1)^2 - Greece Juniors 1987 p3
x^{n+1}+ax+b divisible by (x-1)^2 - Greece Juniors 1987 p3
Source:
September 13, 2024
algebra
polynomial
Problem Statement
Find real
a
,
b
a,b
a
,
b
such that polynomial
P
(
x
)
=
x
n
+
1
+
a
x
+
b
P(x)=x^{n+1}+ax+b
P
(
x
)
=
x
n
+
1
+
a
x
+
b
to be divisible by
(
x
−
1
)
2
(x-1)^2
(
x
−
1
)
2
. Then find the quotient
P
(
x
)
:
(
x
−
1
)
2
,
n
∈
N
∗
P(x):(x-1)^2 , n\in \mathbb{N}^*
P
(
x
)
:
(
x
−
1
)
2
,
n
∈
N
∗
Back to Problems
View on AoPS