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From: lloyd on 18 Jul 2010 14:03
I don't have much knowledge of number theory and I haven't been able
to find information about this--could someone send a pointer, it would
be much appreciated?

The multiplicative cycle of a primitive root mod n features all
possible differences between successive members before returning to
its starting point. I'd just like a hint as to why this happens.

Example, mod 19, powers of 3:

1,3,9,8,5,15,7,2,6... has differences 2,6,18,16,10,11,14,4... and
never repeats a difference until we get back to 1.

Thank you!

From: bert on 18 Jul 2010 15:25
On 18 July, 19:03, lloyd <lloyd.hough...(a)gmail.com> wrote:
> I don't have much knowledge of number theory and I haven't been able
> to find information about this--could someone send a pointer, it would
> be much appreciated?
>
> The multiplicative cycle of a primitive root mod n features all
> possible differences between successive members before returning to
> its starting point. I'd just like a hint as to why this happens.
>
> Example, mod 19, powers of 3:
>
> 1,3,9,8,5,15,7,2,6... has differences 2,6,18,16,10,11,14,4... and
> never repeats a difference until we get back to 1.

Starting from any member 'b', the
difference to the next is b(a-1),
where 'a' is the primitive root.

So if the differences differ for
every member, and every member is
different, then every difference
is different, too. Pardon the
tangled language!
--
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