For each positive integer $n$ denote: \[n!=1\cdot 2\cdot 3\dots n\]Find all positive integers $n$ for which $1!+2!+3!+\cdots+n!$ is a perfect square.
Source: 2022 Grosman Mathematical Olympiad P1
Tags: factorial, number theory
For each positive integer $n$ denote: \[n!=1\cdot 2\cdot 3\dots n\]Find all positive integers $n$ for which $1!+2!+3!+\cdots+n!$ is a perfect square.