# Lucky Number 17!

Number Theory Level 5

Find the remainder when the number below is divided by 17.

$\large 1^{1!} + 2^{2!} + 3^{3!} + 4^{4!} + \cdots + 17^{17!}$

Notation:
$$!$$ denotes the factorial notation. For example, $$10! = 1\times2\times3\times\cdots\times10$$.

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