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Factors of Positive Integers

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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Ray Paseur
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Ray Paseur
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1 Solution
 
d-glitchCommented:
No.  The proof is in modular arithmetic.
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d-glitchCommented:
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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d-glitchCommented:
This is 1st year college Number Theory, not 6th grade arithmetic.
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Ray PaseurAuthor Commented:
Thanks.  I was going to test all the numbers but figured a proof would save time :-)
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