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From: budd@ihlpf.UUCP
Newsgroups: net.math
Subject: "Re: prime numbers (high school math) - (nf)"
Message-ID: <195@ihlpf.UUCP>
Date: Wed, 26-Oct-83 22:57:10 EDT
Article-I.D.: ihlpf.195
Posted: Wed Oct 26 22:57:10 1983
Date-Received: Fri, 28-Oct-83 08:40:56 EDT
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#R:arizona:-558700:ihlpf:6200019:  0:371
ihlpf!dap1    Oct 24 19:46:00 1983

The second result is easy.  It's the same as saying that

n^2 - 1 = (n - 1)(n + 1) | 24 = 3*4*2  ('|' means divisibility).

Since n is prime and greater than 5, we know that:

a. one of n-1 or n+1 is divisible by three.

b. one of n-1 or n+1 is divisible by two

c. one of n-1 or n+1 is divisible by four.

So the whole thing is divisible by 24.

Darrell Plank
Bell Labs