Below are some practice problems with a
subjective rating on difficulties. The solutions are included at the
end of Math Olympiad part of LibreNotebook.
0.1.1. 1996 Ireland Problem
8 (\( \bullet \bullet \circ
\)) Given a prime \(p\) and \(a,
n \in \mathbb {N}\), show that if \(2^p + 3^p = a^n\), then \(n = 1\).