Introduction

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

A chapter in Representations of Integers as Sums of Squares, 1985, pp 1-4 from Springer

Abstract: Abstract What do the relations (i) $$ {5^2} = {3^2} + {4^2} $$ (ii) $$ 6 = {1^2} + {1^2} + {1^2} + {1^2} + {1^2} + {1^2} = {2^2} + {1^2} + {1^2} $$ (iii) $$ 7 \ne {a^2} + {b^2} + {c^2} $$ have in common? Obviously, their right hand members are all sums of squares. One way to describe those relations is as follows: i The square 52 can be represented, in essentially one way only, as the sum of two squares, ii The integer 6 can be represented in (at least) two essentially distinct ways as a sum of squares. iii The integer 7 cannot be represented as a sum of three squares.

Keywords: Theta Function; Algebraic Number; Quadratic Residue; Rational Integer; Algebraic Number Theory (search for similar items in EconPapers)
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_1

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

DOI: 10.1007/978-1-4613-8566-0_1

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 ().