Problem

Source: 239 MO (8-9).2/(10-11).3

Tags: number theory



Given are two distinct sequences of positive integers $(a_n)$ and $(b_n)$, such that their first two members are coprime and smaller than $1000$, and each of the next members is the sum of the previous two. 8-9 grade Prove that if $a_n$ is divisible by $b_n$, then $n<50$ 10-11 grade Prove that if $a_n^{100}$ is divisible by $b_n$ then $n<5000$