17 necessary and sufficient conditions for the primality of Fermat numbers

Michal Křížek; Lawrence Somer

Acta Mathematica et Informatica Universitatis Ostraviensis (2003)

  • Volume: 11, Issue: 1, page 73-79
  • ISSN: 1804-1388

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Křížek, Michal, and Somer, Lawrence. "17 necessary and sufficient conditions for the primality of Fermat numbers." Acta Mathematica et Informatica Universitatis Ostraviensis 11.1 (2003): 73-79. <http://eudml.org/doc/23873>.

@article{Křížek2003,
author = {Křížek, Michal, Somer, Lawrence},
journal = {Acta Mathematica et Informatica Universitatis Ostraviensis},
language = {eng},
number = {1},
pages = {73-79},
publisher = {University of Ostrava},
title = {17 necessary and sufficient conditions for the primality of Fermat numbers},
url = {http://eudml.org/doc/23873},
volume = {11},
year = {2003},
}

TY - JOUR
AU - Křížek, Michal
AU - Somer, Lawrence
TI - 17 necessary and sufficient conditions for the primality of Fermat numbers
JO - Acta Mathematica et Informatica Universitatis Ostraviensis
PY - 2003
PB - University of Ostrava
VL - 11
IS - 1
SP - 73
EP - 79
LA - eng
UR - http://eudml.org/doc/23873
ER -

References

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  6. Křížek M., Chleboun J., A note on factorization of the Fermat numbers and their factors of the form 3 h 2 n + 1 , Math. Bohem. 119, 1994, 437-445. (1994) MR1316595
  7. Křížek M., Luca F., Somer L., 17 lectures on the Fermat numbers. From number theory to geometry, Springer-Verlag, New York 2001. MR1866957
  8. Křížek M., Somer L., A necessary and sufficient condition for the primality of Fermat numbers, Math. Bohem. 126, 2001, 541-549. MR1970256
  9. Luca F., Fermat numbers and Heron triangles with prime power sides, Amer. Math. Monthly, accepted in 2000. 
  10. Lucas E., Theoremes d'arithmétique, Atti della Reale Accademia delle Scienze di Torino 13, 1878, 271-284. 
  11. Mcintosh R., 10.2307/2975806, Amer. Math. Monthly 90, 1983, 98-99. (1983) Zbl0513.10012MR0691180DOI10.2307/2975806
  12. Morehead J. C., 10.1090/S0002-9904-1905-01255-6, Bull. Amer. Math. Soc. 11, 1905, 543-545. (1905) MR1558255DOI10.1090/S0002-9904-1905-01255-6
  13. Pepin P., Sur la formule 2 2 n + 1 , C. R. Acad. Sci. 85, 1877, 329-331. 
  14. Somer L., Křížek M., On a connection of number theory with graph theory, Czechoslovak Math. J. (submitted) MR2059267
  15. Szalay L., A discrete iteration in number theory, (Hungarian), BDTF Tud, Kozi. VIII. Termeszettudomanyok 3., Szombathely, 1992, 71-91. (1992) Zbl0801.11011
  16. Vasilenko O. N., On some properties of Fermat numbers, (Russian), Vestnik Moskov. Univ. Ser. I Mat. Mekh., no. 5 1998, 56-58. (1998) Zbl1061.11500MR1708238
  17. Wantzel P. L., Recherches sur les moyens de reconnaitre si un Probleme de Geometrie peut se resoudre avec la regie et le compas, J. Math. 2, 1837, 366-372. 

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