Integers as sum of squares

• Main Authors: Calusin, Rosalie Coney E., Castro, Marilen M.
• Format: text
• Language: English
• Published: Animo Repository 1995
• Subjects: Number theory; Trigonometric sums; Square; Congruences and residues
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16243
• Institution: De La Salle University

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.