MathDB

The n-th term of a sequence is coprime with n

Source: Italian National Olympiad 2007, problem 5

May 13, 2007

number theory proposednumber theory

Problem Statement

The sequence of integers

(a_{n})_{n \ge 1}

is defined by

a_{1}= 2

,

a_{n+1}= 2a_{n}^{2}-1

. Prove that for each positive integer n,

n

and

a_{n}

are coprime.

Back to Problems View on AoPS