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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


A deterministic algorithm for solving $n=fu^ 2+gv^ 2$ in coprime integers $u$ and $v$
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by Kenneth Hardy, Joseph B. Muskat and Kenneth S. Williams PDF
Math. Comp. 55 (1990), 327-343 Request permission


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.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 55 (1990), 327-343
  • MSC: Primary 11Y50; Secondary 11D09
  • DOI:
  • MathSciNet review: 1023762