Southeast Asian Bulletin of Mathematics

, Volume 25, Issue 1, pp 111–115

Another Note on the Greatest Prime Factors of Fermat Numbers

Original articles

DOI: 10.1007/s10012-001-0111-4

Cite this article as:
Grytczuk, A., Wójtowicz, M. & Luca, F. SEA bull. math. (2001) 25: 111. doi:10.1007/s10012-001-0111-4


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.


Fermat numbergreatest prime factorlinear forms in p-adic logarithms

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