MathDB

Easy

Source: Iran 2004

September 14, 2004

algebraInteger PolynomialInteger sequence

Problem Statement

Suppose

f

is a polynomial in

\mathbb{Z}[X]

and m is integer .Consider the sequence

a_i

like this

a_1=m

and

a_{i+1}=f(a_i)

find all polynomials

f

and alll integers

m

that for each

i

:

a_i | a_{i+1}

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