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https://hdl.handle.net/2142/86966
Description
Title
Some Extremal Problems in Additive Number Theory
Author(s)
Brueggeman, Jeffrey Alan
Issue Date
1998
Doctoral Committee Chair(s)
Hildebrand, A.J.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
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 .
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