May 23rd, 2009, 04:48 PM  #1 
Newbie Joined: May 2009 Posts: 5 Thanks: 0  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. 
May 23rd, 2009, 05:17 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  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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