A number theory problem by A P

Number Theory Level pending

What is the smallest natural number k > 1 k > 1 that has the property that k ! k! has k k digits?

Notation : ! ! denotes the factorial notation. For example, 8 ! = 1 × 2 × 3 × × 8 8! = 1\times2\times3\times\cdots\times8 .


The answer is 22.

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