Variants of the Brocard-Ramanujan equation

Omar Kihel[1]; Florian Luca[2]

  • [1] Department of Mathematics Brock University 500 Glenridge Avenue St. Catharines, Ontario Canada L2S 3A1 00000
  • [2] Mathematical Institute UNAM, Campus Morelia Apartado, Postal 27-3 (Xangari), C.P. 58089 Morelia, Michoacán, Mexico

Journal de Théorie des Nombres de Bordeaux (2008)

  • Volume: 20, Issue: 2, page 353-363
  • ISSN: 1246-7405

Abstract

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In this paper, we discuss variations on the Brocard-Ramanujan Diophantine equation.

How to cite

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Kihel, Omar, and Luca, Florian. "Variants of the Brocard-Ramanujan equation." Journal de Théorie des Nombres de Bordeaux 20.2 (2008): 353-363. <http://eudml.org/doc/10840>.

@article{Kihel2008,
abstract = {In this paper, we discuss variations on the Brocard-Ramanujan Diophantine equation.},
affiliation = {Department of Mathematics Brock University 500 Glenridge Avenue St. Catharines, Ontario Canada L2S 3A1 00000; Mathematical Institute UNAM, Campus Morelia Apartado, Postal 27-3 (Xangari), C.P. 58089 Morelia, Michoacán, Mexico},
author = {Kihel, Omar, Luca, Florian},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Brocard-Ramanujan problem; Diophantine equation involving factorials; ABC conjecture},
language = {eng},
number = {2},
pages = {353-363},
publisher = {Université Bordeaux 1},
title = {Variants of the Brocard-Ramanujan equation},
url = {http://eudml.org/doc/10840},
volume = {20},
year = {2008},
}

TY - JOUR
AU - Kihel, Omar
AU - Luca, Florian
TI - Variants of the Brocard-Ramanujan equation
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2008
PB - Université Bordeaux 1
VL - 20
IS - 2
SP - 353
EP - 363
AB - In this paper, we discuss variations on the Brocard-Ramanujan Diophantine equation.
LA - eng
KW - Brocard-Ramanujan problem; Diophantine equation involving factorials; ABC conjecture
UR - http://eudml.org/doc/10840
ER -

References

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  2. D. Berend, J.E. Harmse, On polynomial-factorial diophantine equations. Trans. Amer. Math. Soc. 358 (2005), no 4, 1741–1779. Zbl1114.11029MR2186995
  3. B.C. Berndt, W.F. Galway, On the Brocard-Ramanujan Diophantine equation n ! + 1 = m 2 . The Ramanujan Journal 4 (2000), 41–42. Zbl0999.11078MR1754629
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  10. E. Landau, Handbuch der Lehre von der verteilung der Primzahlen, 3rd Edition. Chelsea Publ. Co., 1974. Zbl40.0232.08
  11. F. Luca, The Diophantine equation P ( x ) = n ! and a result of M. Overholt. Glas. Mat. Ser. III 37 (57) no. 2 (2002), 269–273. Zbl1085.11023MR1951531
  12. H.L. Montogomery, R.C. Vaughan, The large sieve. Mathematika 20 (1973), 119–134. Zbl0296.10023MR374060
  13. M. Overholt, The diophantine equation n ! + 1 = m 2 . Bull. London Math. Soc. 25 (1993), 104. Zbl0805.11030MR1204060
  14. R. M. Pollack, H. N. Shapiro, The next to last case of a factorial diophantine equation. Comm. Pure Appl. Math. 26 (1973), 313–325. Zbl0276.10011MR360465
  15. S. Ramanujan, Question 469. J. Indian Math. Soc. 5 (1913), 59. 
  16. S. Ramanujan, Collected papers. New York, 1962. 
  17. S. Wolfram, Math World. http://mathworld.wolfram.com/WilsonTheorem.html 

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