MathNet 2026 — Part 06 Question 81

For $n$ a positive integer, $n! = 1 \cdot 2 \cdot 3 \cdots (n-1) \cdot n$ is the product of the positive integers from 1 to $n$. Determine, with proof, all positive integers $n$ for which $n! + 3$ is a power of 3.