Integers as sum of squares

Date of Publication

1995

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Abstract/Summary

This paper delt on the representation of integers as the sum of two or more than two squares. A natural question to ask is What is the smallest positive integer n such that every positive integer can be represented as sum of not more than n squares? Theorems, lemmas, and corollaries that support the following results provide the answer to this inquiry.(a) Prime of the form 4k + 1 can be expressed uniquely as sum of two squares, (b) Integers of the form n = N2m, where m is square-free, can be represented as sum of two squares if and onlyif m contains no prime factor of the form 4k + 3, (c) Integers having prime factors of the form 4k + 3 raised to an even power can be expressed as sum of two squares, (d) No positive integer of the form 4 n (8m + 7) can be represented as sum of three squares, (3) Any positive integer n can be represented as sum of four squares, some of which may be zero.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU07044

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

101 leaves

Keywords

Number theory; Trigonometric sums; Square; Congruences and residues

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