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May 5th, 2013, 10:09 AM   #1
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Little LCM lemma for the first n pronics

Pronics are of course numbers of the form (x)(x+1). The first pronic can for different purposes be considered 0*1 or 1*2. In this case, I am going with 1*2 as the first pronic.

First n pronics will therefore be 1*2, 2*3, ..., n(n+1)

ALL pronics are even, as one of n and n+1 is always even. But there is no other common factor to all n of the first n pronics, even when you consider only the first 2, ie 1*2 and 2*3.

So the LCM of the of the first n pronics will always be (n+1)!/2

eg, for the first 4, ie 1*2, 2*3, 3*4, 4*5, it is 5!/2 or 60.

Did I screw anything up? Pretty sure I didn't, but would appreciate a check off!

(This will I hope be part of a larger if not exactly profound proof concerning pronics and harmonic means.)
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May 5th, 2013, 10:32 AM   #2
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Re: Little LCM lemma for the first n pronics

Quote:
Originally Posted by johnr
Did I screw anything up? Pretty sure I didn't, but would appreciate a check off!
I don't see any errors, it looks fine!
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May 5th, 2013, 10:34 AM   #3
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Re: Little LCM lemma for the first n pronics

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Originally Posted by mathbalarka
Quote:
Originally Posted by johnr
Did I screw anything up? Pretty sure I didn't, but would appreciate a check off!
I don't see any errors, it looks fine!
Thanks!
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