Another Note on the Greatest Prime Factors of Fermat Numbers (original) (raw)

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 = 22_m_ + 1 is the m_‘th Fermat number, then P(F m ) ≥ 2_m+2(4_m_ + 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 = a_2_m + 1 whenever a is even and m ≥ _a_18.

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Authors and Affiliations

  1. Institute of Mathematics, T. Kotarbiński Pedagogical University, 65-069, Zielona Góra, Pl. Slowiański 9, Poland
    A. Grytczuk & M. Wójtowicz
  2. Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
    F. Luca

Authors

  1. A. Grytczuk
  2. M. Wójtowicz
  3. F. Luca

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Correspondence toA. Grytczuk.

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AMS Subject Classification (1991) 11A51 11J86

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Grytczuk, A., Wójtowicz, M. & Luca, F. Another Note on the Greatest Prime Factors of Fermat Numbers.SEA bull. math. 25, 111–115 (2001). https://doi.org/10.1007/s10012-001-0111-4

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