On Prielipp's Problem on Signed Sums ofkth Powers

✍ Scribed by Michael N. Bleicher

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 489 KB
• Volume: 56
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1996.0004

✦ Synopsis

where m is a positive integer, depending on n and the = i are all either \1 the particular choices of the = i depending on n and m. Among other things we prove such a representation always exists; in fact, infinitely many exist. The proof is algorithmic, so that a polynomial time method of finding the representation is presented. We get asymptotic estimates for the minimal value of m, in each of the cases (a) k fixed and n grows to infinity and (b) n fixed and k grows to infinity. A number of related problems and conjectures are also presented.

1996 Academic Press, Inc. n i=1 = i a i , where the = i have their values restricted to a given set. Various questions may be asked; some are indicated below: article no.