|
Infinite families of solutions of the equation
Author(s):
P.
Goetgheluck.
Journal:
Math. Comp.
67
(1998),
1727-1733.
MSC (1991):
Primary 11B65, 11Y50, 11B37
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We give explicit formulas providing two new infinite families of couples of binomial coefficients whose ratio is 2.
References:
- 1.
- A. D. Barry, L'équation diophantienne
, Enseign. Math. (2) 25 (1979), 23-31. MR 81b:10006 - 2.
- P. Goetgheluck, Computing binomial coefficients, Amer. Math. Monthly 94 (1987), 360-365.
- 3.
- -, On prime divisors of binomial coefficients, Math. Comp., 51 (1988), 325-329. MR 89f:11033
- 4.
- C. G. Khatri and A. M. Vaidya, On integers which are ratios of two triangular numbers, J. Indian Math. Soc. (N.S.) 35 (1971), 205-215. MR 46:7157
- 5.
- E. E. Kummer, Uber die Erganzumgssatze zu den allgemeinen Reciprocität gesetzen, J. Reine Angew. Math. 44 (1852), 93-164.
- 6.
- W. J. Le Veque, Topics in Number Theory, Vol. 1, Addison-Wesley, Reading, MA, 1956. MR 18:283d
- 7.
- L. J. Mordell, Diophantine Equations, Academic Press, London, 1969. MR 40:2600
- 8.
- C. D. Olds, Continued Fractions, Random House, New York, 1963. MR 26:3672
- 9.
- T. N. Shorey, On the ratio of values of a polynomial, Proc. Indian Acad. Sci. (Math. Sci.) 93 (1984), 109-116. MR 87c:11037
- 10.
- D. Singmaster, Repeated binomial coefficients and Fibonacci numbers, Fibonacci Quarterly 13 (1975), 295-298. MR 54:224
- 11.
- S. Thouvenot, Résolution en nombres entiers de l'équation diophantienne
, Enseign. Math. (2) 16 (1970), 203-217. MR 45:3319 - 12.
- B. M. M. de Weger, Equal binomial coefficients: Some elementary considerations, J. Number Theory, 63 (1997), 373-386. MR 98b:11027
Similar Articles:
Retrieve articles in Mathematics of Computation
with MSC
(1991):
11B65, 11Y50, 11B37
Retrieve articles in all Journals with MSC
(1991):
11B65, 11Y50, 11B37
Additional Information:
P.
Goetgheluck
Affiliation:
Université de Paris-Sud, Mathématiques, Bat 425, 91405 Orsay Cedex, France
Email:
goetghe@iut-orsay.fr
DOI:
10.1090/S0025-5718-98-01002-3
PII:
S 0025-5718(98)01002-3
Received by editor(s):
May 29, 1996
Received by editor(s) in revised form:
October 7, 1996
Copyright of article:
Copyright
1998,
American Mathematical Society
|