Katabatak Powers

[Turtle]

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Edited September 21, 2013 by Turtle

[belovelife]

i am unfamiliar with these

could you define please

[Don Blazys]

Interesting. Now we have a palindromic pattern of last digits that is eleven digits long and does not contain 2, 6, 7 or 8.

 

Don.

[Don Blazys]

The even exponents give us eight digit palindromic patterns while the odd exponents do not. That's "odd".

 

The exponents (2 and 8), (3 and 9), and (4 and 10) result in the exact same patterns. That's "even odder". (I know... "even odder" is bad grammar... but I like the "play on words" and the way it sounds! Try saying it really fast four or five times in a row!)

[Qfwfq]

it appears this length is "long" if the divisor is prime, and "short" if the divisor is composite.

Methinks you're wanting to look up the topic of finite fields, in paticular of [imath]\mathbb{Z}_p[/imath] in comparison to any other [imath]\mathbb{Z}_n[/imath] (where [imath]p, n\in\mathbb{N}[/imath] but [imath]p[/imath] is also prime).

 

The short shot is that, in the fields, 0 is the only divisor of 0...

[Qfwfq]

roger. will read up. is this a "solution" to the mystery, or rather symbology to represent it?

Gosh, I'm not sure exactly how the problem is stated now.

[Qfwfq]

that lean versing prompts me to ask, "aren't the ranges of the katabatak/digital root function rings & not fields?", as we cannot sensibly divide the range elements by one-another.

That is pretty much the point, [imath]\mathbb{Z}_n[/imath] is always a ring; a necessary and sufficient condition in order for it to also be a field is for [imath]n[/imath] to be prime.

[DFINITLYDISTRUBD]

I Bump thee!

Back from the near dead the greatest mathematical thread since Bucky Fulster!!!!

[DFINITLYDISTRUBD]

So much stuff missing here.....Oh well the missing bits still live here http://scienceforums.com/topic/1304-katabatak-math-an-exploration-in-pure-number-theory/

[DFINITLYDISTRUBD]

For now anyway maintaining a link to the other thread for reference is no biggie...it opens in a new window so, for instance if one needs an explanation to what a katabatak is a link is not something that has to be chased down. Shame there's no way to cleanly and easily merge the two.