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From: stan@clyde.UUCP
Newsgroups: net.math
Subject: Re: Simple Division Properties
Message-ID: <107@clyde.UUCP>
Date: Thu, 25-Aug-83 09:42:47 EDT
Article-I.D.: clyde.107
Posted: Thu Aug 25 09:42:47 1983
Date-Received: Thu, 25-Aug-83 21:54:58 EDT
References: <548@uw-june>
Organization: Bell Labs Whippany NJ
Lines: 13

If N is the number and r is the radix,

(All the digits of N added together)  mod (r-1)  =  N mod (r-1)

Can anyone here supply a proof?

P.S.  This means it is easy to test binary numbers for divisibility
by 3 (r-1=2**2-1), 7 (r-1=2**3-1), 15 (r-1=2**4-1), and so on.
Especially helpful for hardware.

		Stan King			phone: 201-386-7433
		Bell Labs, Whippany, NJ		Cornet:  8+232-7433
		room 2A-111			uucp:	 clyde!stan