Use the fact that for all integers n, n!=n(n1)...321. An

Chapter 4, Problem 4.289

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Use the fact that for all integers n, n!=n(n1)...321. An alternative proof of the innitude of the prime numbers begins as follows: Proof: Suppose there are only nitely many prime numbers.Thenoneisthelargest.Callit p.LetM = p!+1.We will show that there is a prime number q such that q > p. Complete this proof.

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