MathDB

ASU 485 All Soviet Union MO 1988 a_0 = 0, a_n = p(a_n-1), p(x) pos.integer pol

Source:

August 8, 2019

polynomialInteger sequenceSequencegreatest common divisor

Problem Statement

The sequence of integers an is given by

a_0 = 0, a_n = p(a_n-1)

, where

p(x)

is a polynomial whose coefficients are all positive integers. Show that for any two positive integers

m, k

with greatest common divisor

d

, the greatest common divisor of

a_m

and

a_k

a_d