Re: Divisibility by 7 & 13

From: Arturo Magidin (magidin_at_math.berkeley.edu)
Date: 02/25/05 

Date: Fri, 25 Feb 2005 16:50:00 +0000 (UTC)

In article <200502251442.j1PEg2u06735@proapp.mathforum.org>,
Rajinder Goswami <rajindergoswami@hotmail.com> wrote:

>I have developed a new and very easy method to find out divisibility
 by 7 & 13.

They may not be new, but sure.

>The exisitng methods for divisibilty for 7 is :- take the last digit,
 multiply it with 2 and subtract the result from remaining number. We
 are to repeat the process till all the digits are exhuasted

This is but one method to check divisibility by 7. Many others
exist. There was a Martin Gardner column that included several methods
(it is where I learned the method you mention). That might be a good
place to start.

(And if the MAA ever actually gets around to publishing their CD-ROM
with all of Gardner's columns, which they have been promising since
December but is still not out, it will be easy to check).

>For 13 :- take the last digit, multiply it with 4 and add the result
 to remaining number. Again, in this method, we are to repeat the
 process till all the digits are exhusted.

You don't have to repeat it until all the digits are exhausted; you
just have to repeat it until you get to a number which is either
obviously divisible or obviously not divisible by 7 (resp. 13).

>I have found out a simpler and better way. I want to get it published
 in a good journal. Will you please be kind enough to suggest me how I
 should proceed?

First, write it up carefully and justify it. Then circulate it among
mathematicians to make sure it is correct; if it is either unknown or
obscure, try either a note in the American Mathematical Monthly or the
Mathematics Magazine, both published by the MAA. 

-- 
======================================================================
"It's not denial. I'm just very selective about
 what I accept as reality."
    --- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu

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