MathDB

a_n = gcd(a_{n+k}, a_{n+k+1}) for all n, sequence a_n

Source: Dutch BxMO TST 2019 p4

January 10, 2020

GCDnumber theorygreatest common divisorSequence

Problem Statement

Do there exist a positive integer

k

and a non-constant sequence

a_1, a_2, a_3, ...

of positive integers such that

a_n = gcd(a_{n+k}, a_{n+k+1})

for all positive integers

n