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.
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References
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.
C. P. Wrathall,New Factors of Fermat Numbers, Math. Comp., vol. 18, 1964, p. 324–325.
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.
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Riesel, H. Common prime factors of the numbers\(A_n = a^{2^n } + 1\) . BIT 9, 264–269 (1969). https://doi.org/10.1007/BF01946818
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DOI: https://doi.org/10.1007/BF01946818