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From: leo@ihuxl.UUCP
Newsgroups: net.math
Subject: Proof of divide by 3 rule
Message-ID: <510@ihuxl.UUCP>
Date: Fri, 26-Aug-83 12:18:17 EDT
Article-I.D.: ihuxl.510
Posted: Fri Aug 26 12:18:17 1983
Date-Received: Sat, 27-Aug-83 19:41:35 EDT
Organization: BTL Naperville, Il.
Lines: 18


If you don't know what modular arithmetic is, read no further.

The proof of the divide by three rule is pretty simple.
I present it here as a more general proof.

        Consider number with k digits  (abcdef...)
        This number is a*(r**k)+b*(r**(k-1))+...
        By the above lemma, it is then equivalent to

        This proves both the rules for 9 and 3, since
        10 = 1 modulo 3 and 10 = 1 modulo 9.
        For the REAL hackers, it should be noted that
        the divide by 3 rule also works in hex since
        16 = 1 modulo 3.

                        Leo R.
			ihuxl!leo