 # Representation of integers as sum of squares.

## ESIRC/Manakin Repository

 dc.contributor.author Ismail, Rashidah. dc.date.accessioned 2012-07-12T20:37:43Z dc.date.available 2012-07-12T20:37:43Z dc.date.created 1989 en_US dc.date.issued 2012-07-12 dc.identifier.uri http://hdl.handle.net/123456789/1875 dc.description 134 leaves en_US dc.description.abstract The purpose of this thesis is to investigate the problem of representing aninteger as sum of two, three, and four squares. First the necessary and Sufficient conditions for an integer to be representable as the sum of two and four squares are considered. Then I investigate the problem of the representation of integers as a sum of two and four nonvanishing squares. Next the problem of representing integers as a sum of two and four unequal squares is studied. The uniqueness of representations is also be discussed. Formulas for the total number of representation of an integer as a sum of two and four squares are given. For the sum of three squares problem I characterize the integers that can be represented as a sum of three squares, and only give formulas without proofs for the number of representations of an integer as a sum of three squares, since their proofs are beyond the scope of this thesis. en_US dc.language.iso en_US en_US dc.subject Numbers, Natural. en_US dc.subject Sequences (Mathematics) en_US dc.subject Forms, Quadratic. en_US dc.title Representation of integers as sum of squares. en_US dc.type Thesis en_US dc.college las en_US dc.advisor Essam A. Abotteen en_US dc.department mathematics, computer science, and economics en_US