[net.math] Proof of divide by 3 rule

leo@ihuxl.UUCP (08/26/83)

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