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


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.


Computational Mathematic Fermat Common Factor Prime Factor Fermat Number 
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  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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