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I'll just preface this by saying I'm just a physics undergrad, so this might be a bit beyond my understanding, and I may well be missing something obvious or making a stupid mistake, but while playing around I noticed that it seems to be true that

Is this actually true? And if so is there a proof of it I'll be able to wrap my mind around?

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04/03/2010, 12:18 AM
(This post was last modified: 04/03/2010, 12:18 AM by Stereotomy.)
(04/02/2010, 10:57 PM)bo198214 Wrote: (04/02/2010, 07:16 PM)Stereotomy Wrote:

Is this actually true? And if so is there a proof of it I'll be able to wrap my mind around?

I dont think it is true. For example:

Ah, good point, though

Is true as well. In fact, thinking about it, the numbers I tried out with this all had b>a. Perhaps that's an additional condition that either b > a or m, n > 1?

Just quickly tried this for a few low examples, a = 8, 9, 10, 11, and it seems to hold.

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(04/03/2010, 12:18 AM)Stereotomy Wrote:

Is true as well. In fact, thinking about it, the numbers I tried out with this all had b>a. Perhaps that's an additional condition that either b > a or m, n > 1?

There is an article which proves that

(which is

in Knuth's arrow notation) finally will be constant for

mod any

, see this

thread.