--- Ignacio Larrosa CaĆ±estro <

ilarrosa@...> wrote:

> Monday, September 04, 2006 6:21 PM [GMT+1=CET],

> Phil Carmody <thefatphil@...> escribiĆ³:

> > I don't suppose anyone can sketch a proof of it, could they?

>

> I think there are two or more versions of the theorem, related I suppose. In

> "Introduction to Analytic Number Theory" of T. M. Apostol, there is this:

>

> If p >= 5 is prime, then

>

> S_{p-2} = Sum((p - 1)!/k, k, 1, p-1) = 0 (mod p^2)

...

> ===> S_{p-2} = 0 (mod p^2) (q.e.d.)

Many thanks Ignacio! The formulation of the theorem I have seen was different,

but closely related (namely the C(2p-1,p-1) one), and hopefully not too much of

a leap from the above.

In particular, I think I noticed that on Dave Rusin's archive of useful

sci.math.* posts, there's a discussion which seems to relate the two

formulations.

I thought I spotted a generalisation (of the other formulation), and wished to

prove it before relying on its truth!

Thanks again,

Phil

() ASCII ribbon campaign () Hopeless ribbon campaign

/\ against HTML mail /\ against gratuitous bloodshed

[stolen with permission from Daniel B. Cristofani]

__________________________________________________

Do You Yahoo!?

Tired of spam? Yahoo! Mail has the best spam protection around

http://mail.yahoo.com