MathDB

a_{n+2 }= a_{n+1} +a_n +k, least k for which a1991 and 1991 not coprime

Source: Romania IMO TST 1991 p2

February 19, 2020

recurrence relationSequencecoprimenumber theory

Problem Statement

The sequence (

a_n

) is defined by

a_1 = a_2 = 1

and

a_{n+2 }= a_{n+1} +a_n +k

, where

k

is a positive integer. Find the least

k

for which

a_{1991}

and

1991

are not coprime.