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

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Found problems: 2

2024 Israel National Olympiad (Gillis), P5
Tags: smallest prime divisor , integer sequence , number theory
For positive integral $k>1$, we let $p(k)$ be its smallest prime divisor. Given an integer $a_1>2$, we define an infinite sequence $a_n$ by $a_{n+1}=a_n^n-1$ for each $n\geq 1$. For which values of $a_1$ is the sequence $p(a_n)$ bounded?

2023 Pan-American Girls’ Mathematical Olympiad, 1
Tags: smallest prime divisor , largest prime divisor , number theory
An integer \(n \geq 2\) is said to be [i]tuanis[/i] if, when you add the smallest prime divisor of \(n\) and the largest prime divisor of \(n\) (these divisors can be the same), you obtain an odd result. Calculate the sum of all [i]tuanis[/i] numbers that are less or equal to \(2023\).