Quadratic Forms Representing All Integers Coprime to 3

Drawing up on the methods developed by Bhargava to prove "The Fifteen Theorem" and expanded by Rouse when handling integer-valued quadratic forms representing odd integers, we show that an integer-valued quadratic form representing all positive integers coprime to 3 up to 290 must represent all positive integers coprime to 3. We further this result by enumerating a list of 31 critical numbers such that representing all numbers on the list guarantees an integer-valued quadratic form represents all positive integers coprime to 3. Finally, we show that no numbers can be removed from this list.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2015

Author dc:creator

• DeBenedetto, Justin Donald

• Local Density

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10339/57168

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/57168