Consecutive Composite NumbersDate: 06/07/2005 at 14:22:39 From: mundip Subject: about consecutive composite integers Hi - I want to know if m > 0 (an integer) is given, then is it possible to find m consecutive composite integers? For example, if m = 2 the numbers could be 8,9; 9,10; 14,15; 15,16; ... if m = 3 the numbers could be 8,9,10; 14,15,16; ... if m = 4 the numbers could be 24,25,26,27; 25,26,27,28; ... and so on. Is this possible for any value of m? Date: 06/13/2005 at 10:11:34 From: Doctor Samuel Subject: Re: about consecutive composite integers Hi Mundip, Given any integer m > 0, (m + 1)! + 2, (m + 1)! + 3, ..., (m + 1)! + m + 1 is a sequence of m consecutive composite integers, so arbitrarily long sequences of such integers exist. Don't hesitate to write again if there's anything about this answer that you don't understand. - Doctor Samuel, The Math Forum http://mathforum.org/dr.math/ |
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