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 m ≥ a18.
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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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DOI: https://doi.org/10.1007/s10012-001-0111-4