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Problems
Contests
National and Regional Contests
Iran Contests
Iran RMM TST
2020 Iran RMM TST
6
6
Part of
2020 Iran RMM TST
Problems
(1)
Find Poly
Source: Iranian RMM TST 2020 Day2 P6
1/14/2020
For all
n
>
1
n>1
n
>
1
. Find all polynomials with complex coefficient and degree more than one such that
(
p
(
x
)
−
x
)
2
(p(x)-x)^2
(
p
(
x
)
−
x
)
2
divides
p
n
(
x
)
−
x
p^n(x)-x
p
n
(
x
)
−
x
. (
p
0
(
x
)
=
x
,
p
i
(
x
)
=
p
(
p
i
−
1
(
x
)
)
p^0(x)=x , p^i(x)=p(p^{i-1}(x))
p
0
(
x
)
=
x
,
p
i
(
x
)
=
p
(
p
i
−
1
(
x
))
)Proposed by Navid Safaie
algebra
polynomial