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Factors of Positive Integers

Posted on 2014-04-17
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Sorry if this is a 6th-grade arithmetic question...

Can consecutive positive integers ever have a common factor greater than one?  Is there a formal proof?

Thanks and regards, ~Ray
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Question by:Ray Paseur
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by:d-glitch
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No.  The proof is in modular arithmetic.
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If P is a factor of N, then N=0 mod P.  
N+1 will always equal 0+1 mod P.

So if P is a factor of N, it can not be a factor of N+1.
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by:d-glitch
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This is 1st year college Number Theory, not 6th grade arithmetic.
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by:Ray Paseur
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Thanks.  I was going to test all the numbers but figured a proof would save time :-)
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