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Determine the possible values of degree of P(x)

Source: Tournament of Towns Spring 2003 - Senior A-Level - Problem 2

June 15, 2011

algebrapolynomialalgebra proposed

Problem Statement

P(x)

is a polynomial with real coefficients such that

P(a_1) = 0, P(a_{i+1}) = a_i

(

i = 1, 2,\ldots

) where

\{a_i\}_{i=1,2,\ldots}

is an infinite sequence of distinct natural numbers. Determine the possible values of degree of

P(x)