From: Nuxxie <nuxxie@linux.rocks>
Subject: Re: Prog Challenge
Newsgroups: comp.os.linux.advocacy
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Date: Fri, 08 Mar 2024 14:20:12 +0000
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On Thu, 07 Mar 2024 21:25:16 -0600, Physfitfreak wrote:

> 
> I don't think the dorks here know such stuff. And the good ones believe
> it's waste of time but what they do (i.e. "fart") is not waste of time.
>

Project Euler, a well respected forum for programmers, doesn't think
that it's a waste of time:

https://projecteuler.net/problem=26


> 
> So I'll go ahead and ruin it for them all :)
> 
> (method of nines)
>

I don't know.  Being a scientist/engineer, I have little background
in number theory.

But, after some research, it is related to the "multiplicative order"
of the denominator.

In Maxima CAS, there is a function that determines the multiplicative
order: zn_order(a, d), where a is the base and d the denominator.

Example:

zn_order(10,31);
15

Thus, 1/31 should have a repeating length of 15, and it does.

zn_order(10,79832137);
516846

1/79832137 should have a repeating length of 516846; I haven't checked.

But it fails for 1/28:

zn_order(10,28);
false

So the method is not totally general.