A deterministic algorithm for solving n = fu2+gv2in coprime integers u and v

Kenneth Hardy; Joseph B. Muskat; Kenneth S. Williams

doi:10.1090/S0025-5718-1990-1023762-3

A deterministic algorithm for solving n = fu²+gv²in coprime integers u and v

Kenneth Hardy
, Joseph B. Muskat
, Kenneth S. Williams

Department of Mathematics

Carleton University

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We give a deterministic algorithm for finding all primitive representations of a natural number n in the form fu²+gv²where f and g are given positive coprime integers, and n ≥ f + g+ 1, (n, fg) = 1. The running time of this algorithm is at most ≥ (n^{1 4}(logn)³(loglogn)(logloglogn)), uniformly in and g.

Original language	English
Pages (from-to)	327-343
Number of pages	17
Journal	Mathematics of Computation
Volume	55
Issue number	191
DOIs	https://doi.org/10.1090/S0025-5718-1990-1023762-3
State	Published - Jul 1990

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title = "A deterministic algorithm for solving n = fu2+gv2in coprime integers u and v",

abstract = "We give a deterministic algorithm for finding all primitive representations of a natural number n in the form fu2+gv2where f and g are given positive coprime integers, and n ≥ f + g+ 1, (n, fg) = 1. The running time of this algorithm is at most ≥ (n1 4(logn)3(loglogn)(logloglogn)), uniformly in and g.",

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N2 - We give a deterministic algorithm for finding all primitive representations of a natural number n in the form fu2+gv2where f and g are given positive coprime integers, and n ≥ f + g+ 1, (n, fg) = 1. The running time of this algorithm is at most ≥ (n1 4(logn)3(loglogn)(logloglogn)), uniformly in and g.

AB - We give a deterministic algorithm for finding all primitive representations of a natural number n in the form fu2+gv2where f and g are given positive coprime integers, and n ≥ f + g+ 1, (n, fg) = 1. The running time of this algorithm is at most ≥ (n1 4(logn)3(loglogn)(logloglogn)), uniformly in and g.

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A deterministic algorithm for solving n = fu²+gv²in coprime integers u and v

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