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KoMaL A Problems
KoMaL A Problems 2020/2021
A. 801
A. 801
Part of
KoMaL A Problems 2020/2021
Problems
(1)
Composition Of Polynomials
Source: KöMaL A. 801
3/24/2022
For which values of positive integer
m
m
m
is it possible to find polynomials
P
,
Q
∈
C
[
x
]
P, Q\in\mathbb{C} [x]
P
,
Q
∈
C
[
x
]
, with degrees at least two, such that
x
(
x
+
1
)
⋯
(
x
+
m
−
1
)
=
P
(
Q
(
x
)
)
.
x(x+1)\cdots(x+m-1)=P(Q(x)).
x
(
x
+
1
)
⋯
(
x
+
m
−
1
)
=
P
(
Q
(
x
))
.
Proposed by Navid Safaei, Tehran
komal
algebra
polynomial