Southeast Asian Bulletin of Mathematics

, Volume 25, Issue 1, pp 111–115 | Cite as

Another Note on the Greatest Prime Factors of Fermat Numbers

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Abstract

For every positive integer k > 1, let P(k) be the largest prime divisor of k. In this note, we show that if Fm = 22m + 1 is the m‘th Fermat number, then P(Fm) ≥ 2m+2(4m + 9) + 1 for all m ≥ 4. We also give a lower bound of a similar type for P(Fa,m), where Fa,m = a2m + 1 whenever a is even and ma18.

Keywords.

Fermat number greatest prime factor linear forms in p-adic logarithms  

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Copyright information

© Springer-Verlag Hong Kong 2001

Authors and Affiliations

  1. 1.Institute of MathematicsT. Kotarbiński Pedagogical UniversityZielona GóraPoland
  2. 2.Institute of MathematicsCzech Academy of SciencesŽitná 25Czech Republic

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