Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On Zsigmondy primes

Author: Moshe Roitman
Journal: Proc. Amer. Math. Soc. 125 (1997), 1913-1919
MSC (1991): Primary 11A41
MathSciNet review: 1402885
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We present simple proofs of Walter Feit's results on large Zsigmondy primes.

References [Enhancements On Off] (What's this?)

  • 1. E. Artin, The orders of the linear groups, Comm. Pure and Appl. Math. 8 (1955), 355-365. Reprinted in Collected Papers, (edited by S. Lang and J. Tate), 387-397, Addison-Wesley, Reading, Mass., 1965. MR 17:12d
  • 2. W. Feit, On large Zsigmondy primes, Proc. Amer. Math. Soc. 102 (1988), 29-36. MR 89b:11009
  • 3. W. Feit, Extensions of cuspidal characters of $GL_m(q)$, Publ. Math. Debrecen 34 (1987), 273-297. MR 89d:20007
  • 4. W. Feit, G.M. Seitz, On finite rational groups and related topics, Illinois J. Math. 33 (1988), 103-131. MR 90a:20016
  • 5. H. Lüneburg, Ein einfacher Beweis für den Satz von Zsigmondy über primitive Primteiler von $A^n-1$, in Geometries and Groups, (edited by M. Aigner and D. Jungnickel), Lect. Notes in Math. 983, 219-222, Springer Verlag, New York, 1981. MR 84d:10006
  • 6. P. Ribenboim, Catalan's conjecture, Academic Press, New York, 1994.
  • 7. P. Ribenboim, The Book of Prime Number Records, Second Edition, Springer Verlag, New York, 1989. MR 90g:11127
  • 8. C. L. Stewart, The greatest prime factor of $a^n-b^n$, Acta Arith. , 26 (1975), 427-433. MR 53:2844
  • 9. C.L. Stewart, Primitive divisors of Lucas and Lehmer numbers, in Transcendence Theory: Advances and Applications, pp. 79-92, Academic Press, New York, 1977. MR 57:16187
  • 10. T.N. Shorey and C. L. Stewart, On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers, Proc. London Math. Soc. 35 (1977), 425-447.
  • 11. T.N. Shorey and C. L. Stewart, On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers, II, J. London Math. Soc. 23 (1981), 17-23. MR 82m:10025
  • 12. A.H. Wedderburn, A theorem on finite algebras, Trans. Amer. Math. Soc. 6 (1905), 349-352.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11A41

Retrieve articles in all journals with MSC (1991): 11A41

Additional Information

Moshe Roitman

Received by editor(s): December 19, 1995
Additional Notes: I thank Yakov Berkovich for suggesting this subject and for useful discussions concerning it.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society