Some Extremal Problems in Additive Number Theory

We consider a measure t(n) for the efficiency of a representation of a large integer n as a sum of distinct squares, defined as the smallest sum of distinct natural numbers whose squares have sum n. Using a modified greedy algorithm, we give a precise asymptotic estimate for t(n) which shows, in particular, that t(n) is very closely approximated by n .

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Brueggeman, Jeffrey Alan

Contributors dc:contributor

• Hildebrand, A.J.

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI9912202

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86966