MathDB

Math Prize 2011 Problem 18

Source:

September 19, 2011

algebrapolynomialquadraticscalculusintegrationnumber theoryrelatively prime

Problem Statement

The polynomial

P

is a quadratic with integer coefficients. For every positive integer

n

, the integers

P(n)

and

P(P(n))

are relatively prime to

n

. If

P(3) = 89

, what is the value of

P(10)