# Just Factorials around

$\large S_n = 1! + 2! + 3! + \ldots + n!$

Suppose for integer $n>3$, we define $S_n$ as above. If $a_n$ is the maximum positive integer that satisfy the equation $\frac{S_n}{24} = a_n + \frac{ \lambda}{24}$ for constant $\lambda$, find the value of $\lambda$.

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