Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!linus!decvax!harpo!gummo!whuxlb!pyuxll!eisx!npoiv!npois!hogpc!houxm!5941ux!dje
From: dje@5941ux.UUCP
Newsgroups: net.math
Subject: Re: interesting division by three property
Message-ID: <378@5941ux.UUCP>
Date: Thu, 25-Aug-83 10:39:12 EDT
Article-I.D.: 5941ux.378
Posted: Thu Aug 25 10:39:12 1983
Date-Received: Thu, 25-Aug-83 21:59:47 EDT
References: aplvax.270
Lines: 17

There is a test for divisibility by 7:

An integer of the form 10t+u (u is 0 to 9, t is unbounded) is divisible by 7
if and only if t-2u is also divisible by 7.

Example:  test 6543210 for divisibility by 7.  6543210 -> 654321 -> 65430
-> 6543 -> 648 -> 48 not divisible by 7.

Example:  6543215 -> 654311 -> 65429 -> 6524 -> 644 -> 56 is divisible by 7.

Proof: (10t+u) - 7(t+u) = 3(t-2u).

Footnote:  10t+u is divisible by 17 if and only if t-5u is.

Dave Ellis / Bell Labs, Piscataway NJ
...!{hocda,ihnp4}!houxm!houxf!5941ux!dje
...!floyd!vax135!ariel!houti!hogpc!houxm!houxf!5941ux!dje