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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.

 

Speeding Fermat’s factoring method
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by James McKee PDF
Math. Comp. 68 (1999), 1729-1737 Request permission

Abstract:

A factoring method is presented which, heuristically, splits composite $n$ in $O(n^{1/4+\epsilon })$ steps. There are two ideas: an integer approximation to $\surd (q/p)$ provides an $O(n^{1/2+\epsilon })$ algorithm in which $n$ is represented as the difference of two rational squares; observing that if a prime $m$ divides a square, then $m^2$ divides that square, a heuristic speed-up to $O(n^{1/4+\epsilon })$ steps is achieved. The method is well-suited for use with small computers: the storage required is negligible, and one never needs to work with numbers larger than $n$ itself.
References
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Additional Information
  • James McKee
  • Affiliation: Pembroke College, Oxford, OX1 1DW, UK
  • Email: jfm@maths.ox.ac.uk
  • Received by editor(s): March 28, 1997
  • Published electronically: March 1, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Math. Comp. 68 (1999), 1729-1737
  • MSC (1991): Primary 11Y05; Secondary 11Y16, 68Q25
  • DOI: https://doi.org/10.1090/S0025-5718-99-01133-3
  • MathSciNet review: 1653962