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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 new factorization technique using quadratic forms
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by D. H. Lehmer and Emma Lehmer PDF
Math. Comp. 28 (1974), 625-635 Request permission


The paper presents a practical method for factoring an arbitrary N by representing N or $\lambda N$ by one of at most three quadratic forms: $\lambda N = {x^2} - D{y^2},\lambda = 1, - 1,2,D = - 1, \pm 2, \pm 3, \pm 6$. These three forms appropriate to N, together with inequalities for y, are given for all N prime to 6. Presently available sieving facilities make the method quite effective and economical for numbers N having 20 to 25 digits. Four examples arising from aliquot series are discussed in detail.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 625-635
  • MSC: Primary 10A25; Secondary 10-04, 10B05
  • DOI:
  • MathSciNet review: 0342458