MathDB

COMC 2011 Problem 12

Source:

November 4, 2012

algebrapolynomialquadratics

Problem Statement

Let

f(x)=x^2-ax+b

, where

a

and

b

are positive integers. (a) Suppose that

a=2

and

b=2

. Determine the set of real roots of

f(x)-x

, and the set of real roots of

f(f(x))-x

. (b) Determine the number of positive integers

(a,b)

with

1\le a,b\le 2011

for which every root of

f(f(x))-x

is an integer.

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