, Volume 25, Issue 1, pp 111-115

Another Note on the Greatest Prime Factors of Fermat Numbers

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 ) ≥ 2 m+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 = a 2m + 1 whenever a is even and ma 18.

AMS Subject Classification (1991) 11A51 11J86