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Path: utzoo!linus!philabs!sdcsvax!ajh
From: ajh@sdcsvax.UUCP (Alan Hu)
Newsgroups: net.math
Subject: Re:  Divisibility
Message-ID: <3711@sdcsvax.UUCP>
Date: Mon, 29-Aug-83 14:51:37 EDT
Article-I.D.: sdcsvax.3711
Posted: Mon Aug 29 14:51:37 1983
Date-Received: Wed, 31-Aug-83 07:47:54 EDT
Organization: U.C. San Diego, CS Dept
Lines: 26

Back in my old Junior High Math Team Days, I had rules for all the
numbers 1-16.  (You had to do those problems fast!)  Since someone
already gave the rule for 7, I think I'll give the rule for 13.
Note:  I am not a number theoretician, and I make no claims as such.
I don't even know if I can prove this.  I was given this rule, and
I accepted it on faith.  It seems to work.

Divisibility by 13:
	A number n is divisible by 13 iff the number
floor(n/10) + 4 * (n mod 10) is divisible by 13.

For example, take 160485
 16048  +  4 * 5 = 16068
  1606  +  4 * 8 =  1638
   163  +  4 * 8 =   195
    19  +  4 * 5 =    39  (If you can't tell by now, you're hopeless!)
     3  +  4 * 9 =    39  (And you deserve to sit here and look at 39's
      . . .		   forever.  By the way, can any of you derive
			   a function to show which numbers won't reduce
			   by this method?  You know the number must be small,
			   because 4 times the units digit must be greater
			   than 9 times the rest of the number.)


					--Alan J. Hu
					  sdcsvax!ajh