MathDB

China TST 2010, Problem 5

Source:

August 28, 2010

inductionnumber theorygreatest common divisoralgebra unsolvedalgebra

Problem Statement

Given integer

a_1\geq 2

. For integer

n\geq 2

, define

a_n

to be the smallest positive integer which is not coprime to

a_{n-1}

and not equal to

a_1,a_2,\cdots, a_{n-1}

. Prove that every positive integer except 1 appears in this sequence

\{a_n\}