Prime Divisors of Shifted Factorials |
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| Authors: | Luca, Florian Shparlinski, Igor E. |
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| Affiliation: | Instituto de Matemáticas, Universidad Nacional Autónoma de México CP 58089, Morelia, Michoacán, México fluca{at}matmor.unam.mx
Department of Computing, Macquarie University Sydney, NSW 2109, Australia igor{at}ics.mq.edu.au |
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| Abstract: | For any positive integer n we let P(n) be the largest primefactor of n. We improve and generalize several results of P.Erd s and C. Stewart on P(n!+1). In particular, we show thatlim supn infin; P(n!+1)/n 2.5, which improves their lower boundof lim supninfin; P(n!+1)/n2. 2000 Mathematics Subject Classification11A05, 11A07, 11J86. |
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