Translator Disclaimer
2017 New algorithms for modular inversion and representation by the form $x^2 + 3xy + y^2$
Christina Doran, Shen Lu, Barry R. Smith
Involve 10(4): 541-554 (2017). DOI: 10.2140/involve.2017.10.541

Abstract

We observe structure in the sequences of quotients and remainders of the Euclidean algorithm with two families of inputs. Analyzing the remainders, we obtain new algorithms for computing modular inverses and representing prime numbers by the binary quadratic form x2 + 3xy + y2 . The Euclidean algorithm is commenced with inputs from one of the families, and the first remainder less than a predetermined size produces the modular inverse or representation.

Citation

Download Citation

Christina Doran. Shen Lu. Barry R. Smith. "New algorithms for modular inversion and representation by the form $x^2 + 3xy + y^2$." Involve 10 (4) 541 - 554, 2017. https://doi.org/10.2140/involve.2017.10.541

Information

Received: 10 September 2013; Revised: 6 May 2015; Accepted: 11 July 2016; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 1359.11005
MathSciNet: MR3630302
Digital Object Identifier: 10.2140/involve.2017.10.541

Subjects:
Primary: 11A05

Rights: Copyright © 2017 Mathematical Sciences Publishers

JOURNAL ARTICLE
14 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.10 • No. 4 • 2017
MSP
Back to Top