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Food For Thought. - Balinares — LiveJournal
Nov. 12th, 2005
04:27 pm -
Food For Thought.
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November 17th, 2005 02:42 pm (UTC)
prime numbers must be odd, barring 2. even * odd = even. even * even = even
even * odd * even = even.
Every third number is a multiple of 3 (for obvious reasons). Every even number is a multiple of 2. So one of the factors of the product (p-1)p(p+1) must be 6 (3*2) .. Since (p-1) (p+1) must both be even, there are 2 multiples of 2. This means that factors must be 3*2*2 (or 12).
Since 3 is the smallest prime (other than 2), p+1 has 2*2 as prime factors. This means that for EVERY case, 3*2*2*2 (one 2 from (p-1) 2 from (p+1), and a 3 from one of those numbers), ... there is a 24 as a factor.
:) That good enough?