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Food For Thought. - Balinares — LiveJournal

Nov. 12th, 2005

04:27 pm - Food For Thought.

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From:kemonotsukai
Date:November 13th, 2005 12:04 am (UTC)
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So, at the first sight it seems very difficult, but in fact it's really easy ^^
What is 24? 24 = 4 * 2 * 3
So we have to proof that (p-1).p.(p+1)=X*(2*3*4)

One of the term must be divisible by 3 since they are consecutive
A prime number superior than 2 is mandatoty an odd number. So (p-1) and (p+1) are par numbers. They are both divisible by 2, and more since they are two consecutive par nimbers, one of the both must be divisible by 4.
So we have the three multiplicators.

Exemples :
3=> 2 * 3 * 4 = 24
5=> 4 * 5 * 6 = (4)* 5 (2 * 3) = 5*24
7=> 6 * 7 * 8 = (2 * 3) * 7 * (4 * 2 )= (2*7)*24 = 14*24
and so on....
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