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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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

Abstract:

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: https://doi.org/10.1090/S0025-5718-1974-0342458-5
  • MathSciNet review: 0342458