MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
IMOC Shortlist
2018-IMOC
A2
A2
Part of
2018-IMOC
Problems
(1)
f1 o g, f2 o g, ... reducible
Source: IMOC 2018 A2
8/15/2021
For arbitrary non-constant polynomials
f
1
(
x
)
,
…
,
f
2018
(
x
)
∈
Z
[
x
]
f_1(x),\ldots,f_{2018}(x)\in\mathbb Z[x]
f
1
(
x
)
,
…
,
f
2018
(
x
)
∈
Z
[
x
]
, is it always possible to find a polynomial
g
(
x
)
∈
Z
[
x
]
g(x)\in\mathbb Z[x]
g
(
x
)
∈
Z
[
x
]
such that
f
1
(
g
(
x
)
)
,
…
,
f
2018
(
g
(
x
)
)
f_1(g(x)),\ldots,f_{2018}(g(x))
f
1
(
g
(
x
))
,
…
,
f
2018
(
g
(
x
))
are all reducible.
polynomial
algebra
irreducibility