MathDB

Easy

Source: Iranian selection test for IMO 2004

June 27, 2004

algebrapolynomiallimitnumber theory proposednumber theory

Problem Statement

p

is a polynomial with integer coefficients and for every natural

n

we have

p(n)>n

x_k

is a sequence that:

x_1=1, x_{i+1}=p(x_i)

for every

N

one of

x_i

is divisible by

N.

Prove that

p(x)=x+1