Re: Prog Challenge

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.