Affirmative. Your conjecture is Waring's Problem, 1770. Proved by Hilbert, 1905. It's finding M and N for a given p that is really hard. On Wed, Sep 22, 2010 at 3:47 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Interesting.
Does this imply the possibility that:
For every integer p > 0 there exists a number N(p) of pth powers, and a minimum M(p) > 0, such that every integer K > M(p) is the sum of N(p) nonnegative pth powers.
?
What is known about this?
--Dan
Rich quoted:
<< arXiv:1009.3983 Date: Tue, 21 Sep 2010 02:24:50 GMT (10kb)
Title: Every even number greater than 454 is the sum of seven cubes Authors: Noam D. Elkies Categories: math.NT Comments: 9 pages MSC-class: Primary 11P05 \\ It is conjectured that every integer N>454 is the sum of seven nonnegative cubes. We prove the conjecture when N is congruent to 2 mod 4. This result, together with a recent proof for 4|N, shows that the conjecture is true for all even N. \\ ( http://arxiv.org/abs/1009.3983 , 10kb)
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