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BIT Numerical Mathematics

, Volume 9, Issue 3, pp 264–269 | Cite as

Common prime factors of the numbers\(A_n = a^{2^n } + 1\)

  • Hans Riesel
Article

Abstract

A method to find certain common factors of numbers of the form\(A_n = a^{2^n } + 1\), when theA n are lacking algebraic factors, is discussed. Using known factors of the Fermat numbers\(F_n = 2^{2^n } + 1\), otherA n , containing these factors, are deduced.

Keywords

Computational Mathematic Fermat Common Factor Prime Factor Fermat Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. M. Robinson,A Report on Primes of the Form k·2 n+1 and on Factors of Fermat numbers, Proc. Am. Math. Soc., vol. 9, 1958, p. 673–681.Google Scholar
  2. 2.
    C. P. Wrathall,New Factors of Fermat Numbers, Math. Comp., vol. 18, 1964, p. 324–325.Google Scholar
  3. 3.
    H. Riesel,Some Factors of the Numbers \(G_n = 6^{2^n } + 1\) and \(H_n = 10^{2^n } + 1\), Math. Comp., vol. 23, 1969, p. 413–415.Google Scholar

Copyright information

© BIT Foundations 1969

Authors and Affiliations

  • Hans Riesel
    • 1
  1. 1.Dept. of Computer SciencesUniversity of StockholmStockholmSweden

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