From: Matthew Moss <matthew.moss@...>
Date: 2008-05-03T03:13:00+09:00
Subject: Re: Reverse Divisible Numbers (#161)



On May 2, 12:25 pm, Matthew Moss <matthew.m...@gmail.com> wrote:
> > 1089 * 9 = 9801
> > 2178 * 4 = 8712
> > 10989 * 9 = 98901
> > 21978 * 4 = 87912
> > 109989 * 9 = 989901
> > 219978 * 4 = 879912
>
> One of the interesting things I found is that those are all divisible
> by 9. I wonder if that is a property of all such numbers?

Actually, I just did a quick-n-dirty proof to myself that this is
actually true.

While not all numbers divisible by 9 are reversible-divisible numbers
(e.g. 81), it is a necessary requirement (still holding to the rules
that the number is not a palindrome and does not end in zero) that the
number be divisible by 9.

So you could save some time by examining only every ninth number.

If anyone is interested in the reason, I'll try and write down my
proof.