Modular Arithmetic

The number of ordered pairs $(m,n)$, $m,n\in{1,2,\ldots,100}$ such that $7^m+7^n$ is divisible by $5$ is

Find the remainder when $X = 1! + 2! + 3! + \cdots + 100!$ is divided by $240$.

The remainder when 2³¹ is divided by 5 is