At the wedding of two Bulgarian nationals in mathematics, every guest who gave a positive integer \(n\), not yet given by another guest, which divides \(3^n-3\) but does not divide \(2^n-2\), received a prize. If there were an infinite number of guests, would the newlyweds theoretically need an infinite number of gifts?
Problem
Source: XIII International Festival of Young Mathematicians Sozopol 2024, Theme for 10-12 grade
Tags: number theory