On Zsigmondy primes
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Publication:4339165
DOI10.1090/S0002-9939-97-03981-6zbMath0914.11002OpenAlexW1710332503MaRDI QIDQ4339165
Publication date: 5 June 1997
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9939-97-03981-6
Congruences; primitive roots; residue systems (11A07) Power residues, reciprocity (11A15) Primes (11A41)
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Cites Work
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- On finite rational groups and related topics
- On Large Zsigmondy Primes
- On Divisors of Fermat, Fibonacci, Lucas and Lehmer Numbers, II
- Ein Einfacher Beweis für den Satz von Zsigmondy über primitive Primeiler von AN-1
- The greatest prime factor of $a^n - b^n$
- On Divisors of Fermat, Fibonacci, Lucas, and Lehmer Numbers
- The orders of the linear groups