This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 2

2021 Balkan MO Shortlist, N2
Tags: shortlist , sequence , recursion , existence , admiration , number theory
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 $a_i = m^2$. [i]Proposed by Nikola Velov, North Macedonia[/i]

2022 Bulgaria EGMO TST, 4
Tags: shortlist , sequence , recursion , existence , admiration , number theory
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 $a_i = m^2$. [i]Proposed by Nikola Velov, North Macedonia[/i]