Southeast Asian Bulletin of Mathematics

, Volume 25, Issue 1, pp 111–115

Another Note on the Greatest Prime Factors of Fermat Numbers

Authors

    • Institute of MathematicsT. Kotarbiński Pedagogical University
  • M. Wójtowicz
    • Institute of MathematicsT. Kotarbiński Pedagogical University
  • F. Luca
    • Institute of MathematicsCzech Academy of Sciences
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

Abstract

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

Keywords.

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

Copyright information

© Springer-Verlag Hong Kong 2001