MathDB

BMO Shortlist 2021 N2

Source: BMO Shortlist 2021

May 8, 2022

Balkanshortlistnumber theorySequencerecursionExistenceadmiration

Problem Statement

Denote by

l(n)

the largest prime divisor of

n

. Let

a_{n+1} = a_n + l(a_n)

be a recursively defined sequence of integers with

a_1 = 2

. Determine all natural numbers

m

such that there exists some

i \in \mathbb{N}

with

a_i = m^2

.
Proposed by Nikola Velov, North Macedonia