show that an integer n > 4, is prime iff it is not a divisor of...

show that an integer n > 4, is prime iff it is not a divisor of (n-1)!

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Expert Solution

Suppose be an such that

Suppose is prime .

divides a number which are only mutiple of i.e.,

All of does divisible by .

does not divisible .

does not divisible by .

Hence is not a divisor of .

Conversely suppose is not a divisor of .

If is not prime then for some with

divides and also divides as

divides .

Hence is prime if and only if it is not a divisor of .

Colby Messinger answered 1 year ago

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