Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A deterministic algorithm for solving $n=fu^ 2+gv^ 2$ in coprime integers $u$ and $v$

Authors: Kenneth Hardy, Joseph B. Muskat and Kenneth S. Williams
Journal: Math. Comp. 55 (1990), 327-343
MSC: Primary 11Y50; Secondary 11D09
MathSciNet review: 1023762
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give a deterministic algorithm for finding all primitive representations of a natural number n in the form $f{u^2} + g{v^2}$, where f and g are given positive coprime integers, and $n \geq f + g + 1$, $(n,fg) = 1$. The running time of this algorithm is at most \[ \mathcal {O}({n^{1/4}}{(\log n)^3}(\log \log n)(\log \log \log n)),\] uniformly in f and g.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11Y50, 11D09

Retrieve articles in all journals with MSC: 11Y50, 11D09

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society