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National and Regional Contests
Iran Contests
Iran MO (3rd Round)
2004 Iran MO (3rd Round)
13
13
Part of
2004 Iran MO (3rd Round)
Problems
(1)
Easy
Source: Iran 2004
9/14/2004
Suppose
f
f
f
is a polynomial in
Z
[
X
]
\mathbb{Z}[X]
Z
[
X
]
and m is integer .Consider the sequence
a
i
a_i
a
i
like this
a
1
=
m
a_1=m
a
1
=
m
and
a
i
+
1
=
f
(
a
i
)
a_{i+1}=f(a_i)
a
i
+
1
=
f
(
a
i
)
find all polynomials
f
f
f
and alll integers
m
m
m
that for each
i
i
i
:
a
i
∣
a
i
+
1
a_i | a_{i+1}
a
i
∣
a
i
+
1
algebra
Integer Polynomial
Integer sequence