Representations of Integers as Sums of Nonvanishing Squares

Emil Grosswald
Additional contact information
Emil Grosswald: Temple University, College of Liberal Arts

Chapter Chapter 6 in Representations of Integers as Sums of Squares, 1985, pp 72-83 from Springer

Abstract: Abstract It is clear that, for k ≥ 4, every nonnegative integer is representable as a sum of k squares. Indeed, one can always write $$ n = \sum\nolimits_{{i = 1}}^4 {x_i^2} + {0^2} + \cdot \cdot \cdot + {0^2} $$ , with an arbitrary number of zeros. On the other hand, the number of representations r k (n) increases very rapidly with n (see Chapter 12), and besides the representations with k — 4 zeros, one usually finds others with fewer zeros or none at all. For example, if k = 5, then 5 = 22 + 12 + 02 + 02 + 02 = 12 + 12 + 12 + 12 + 12.

Date: 1985
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-8566-0_7

Ordering information: This item can be ordered from
http://www.springer.com/9781461385660

DOI: 10.1007/978-1-4613-8566-0_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().