Re: Sums of Consecutive nth Powers

From: William S. Heck (wheck_at_nyc.rr.com)
Date: 01/24/05 

Date: Mon, 24 Jan 2005 01:00:04 +0000 (UTC)

Is this problem known by some particular name?

"Eamon Warnock" <ewarnock@gz.cngb.com> wrote in message
news:ct0tvq$v7c$1@news.ks.uiuc.edu...
> Consider the Diophantine equation
> 1^n + 2^n + 3^n + 4^n + ... + k^n = N^n where n,k > 1
>
> n = 2, k = 24, N = 70 gives the only solution to the cannonball problem.
> n = 3 gives a special case of Catalan's conjecture (which I believe has
> been recently proved).
>
> Has it been proved that there are no solutions for n > 3?
> Thanx.
>
>
> --
> Posted via Mailgate.ORG Server - http://www.Mailgate.ORG
>