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Iran MO (3rd Round)
2004 Iran MO (3rd Round)
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20
Part of
2004 Iran MO (3rd Round)
Problems
(1)
0 or 1 is root of p(x)
Source: Iranian National Olympiad (3rd Round) 2004
1/9/2009
p
(
x
)
p(x)
p
(
x
)
is a polynomial in
Z
[
x
]
\mathbb{Z}[x]
Z
[
x
]
such that for each
m
,
n
∈
N
m,n\in \mathbb{N}
m
,
n
∈
N
there is an integer
a
a
a
such that
n
∣
p
(
a
m
)
n\mid p(a^m)
n
∣
p
(
a
m
)
. Prove that
0
0
0
or
1
1
1
is a root of
p
(
x
)
p(x)
p
(
x
)
.
algebra
polynomial
number theory proposed
number theory