A continued fractions approach to a result of Feit

Robertson, John P. and Matthews, Keith R. (2008) A continued fractions approach to a result of Feit. American Mathematical Monthly, 115 4: 346-349.

Author Robertson, John P.
Matthews, Keith R.
Title A continued fractions approach to a result of Feit
Journal name American Mathematical Monthly  (ERA 2012 Listed)    (ERA 2010 Rank B)   Check publisher's open access policy
Publication date 2008-04
Sub-type Article
Volume number 115
Issue number 4
ISSN 0002-9890; 1930-0972
Start page 346
End page 349
Total pages 4
Place of publication Washington, DC, United States
Publisher Mathematical Association of America
Language eng
Subject 01 Mathematical Sciences
0101 Pure Mathematics
Abstract For primes that can be written as a sum of integer squares, p = asup2 + (2b)sup2, Kaplansky asked whether the binary quadratic for F = xsup2 - pysup2 always represents a and 4b. Feit and Mollin proved the F does always represent a and 4b using the theory of ideals and the class group structure of quadratic orders. Here, Robertson and Matthews present a mathematical approach showing that a standard continued fraction methods give a more elementary answer to Kaplansky's question than the solutions by Feit and Mollin.
Keyword Theorems
Mathematical problems
Algorithms
Quadratic programming
Number theory
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article
Collections: School of Mathematics and Physics
ERA 2012 Admin Only
 
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