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May 23rd, 2009, 04:48 PM   #1
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Question on Primes & G.C.D.'s

Hello again! Here's a question on Primes and Greatest Common Divisors from Section 3.5 of Rosen's "Discrete Math & its Applications").

Prove that for every positive integer n, there are n consecutive composite integers. [Hint: Consider the n consecutive integers starting with (n + 1)! + 2.]

I would like help on this. Please reply with any tips that you may have.

Thank you.
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May 23rd, 2009, 05:17 PM   #2
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Re: Question on Primes & G.C.D.'s

The hint seems to give it away. Can you think of a prime factor of n! + 2? n! + 3? n! + 4? etc.
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