On the diophantine equation n k = x l

K. Győry

Acta Arithmetica (1997)

  • Volume: 80, Issue: 3, page 289-295
  • ISSN: 0065-1036

Abstract

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P. 294, line 14: For “Satz 8” read “Satz 7”, and for “equation (10)” read “equation (13)”.

How to cite

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K. Győry. "On the diophantine equation ${n \atopwithdelims ()k} = x^l$." Acta Arithmetica 80.3 (1997): 289-295. <http://eudml.org/doc/207044>.

@article{K1997,
abstract = {P. 294, line 14: For “Satz 8” read “Satz 7”, and for “equation (10)” read “equation (13)”.},
author = {K. Győry},
journal = {Acta Arithmetica},
keywords = {exponential diophantine equations; binomial coefficients; linear forms in logarithms},
language = {eng},
number = {3},
pages = {289-295},
title = {On the diophantine equation $\{n \atopwithdelims ()k\} = x^l$},
url = {http://eudml.org/doc/207044},
volume = {80},
year = {1997},
}

TY - JOUR
AU - K. Győry
TI - On the diophantine equation ${n \atopwithdelims ()k} = x^l$
JO - Acta Arithmetica
PY - 1997
VL - 80
IS - 3
SP - 289
EP - 295
AB - P. 294, line 14: For “Satz 8” read “Satz 7”, and for “equation (10)” read “equation (13)”.
LA - eng
KW - exponential diophantine equations; binomial coefficients; linear forms in logarithms
UR - http://eudml.org/doc/207044
ER -

References

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  1. [1] M. A. Bennett and B. M. M. de Weger, On the Diophantine equation | a x n - b y n | = 1 , to appear. 
  2. [2] H. Darmon and L. Merel, Winding quotients and some variants of Fermat's Last Theorem, to appear. Zbl0976.11017
  3. [3] P. Dénes, Über die diophantische Gleichung x l + y l = c z l , Acta Math. 88 (1952), 241-251. 
  4. [4] L. E. Dickson, History of the Theory of Numbers, Vol. II, reprinted by Chelsea, New York, 1971. 
  5. [5] P. Erdős, Note on the product of consecutive integers (II), J. London Math. Soc. 14 (1939), 245-249. Zbl65.1145.01
  6. [6] P. Erdős, On a diophantine equation, J. London Math. Soc. 26 (1951), 176-178. Zbl0043.04309
  7. [7] P. Erdős and J. Surányi, Selected Topics in Number Theory, 2nd ed., Szeged, 1996 (in Hungarian). Zbl0095.02904
  8. [8] K. Győry, On the diophantine equations n 2 = a l and n 3 = a l , Mat. Lapok 14 (1963), 322-329 (in Hungarian). 
  9. [9] K. Győry, Über die diophantische Gleichung x p + y p = c z p , Publ. Math. Debrecen 13 (1966), 301-305. Zbl0171.29703
  10. [10] K. Győry, Contributions to the theory of diophantine equations, Ph.D. Thesis, Debrecen, 1966 (in Hungarian). 
  11. [11] E. Landau, Vorlesungen über Zahlentheorie, III, Leipzig, 1927. 
  12. [12] S. Lubelski, Studien über den grossen Fermatschen Satz, Prace Mat.-Fiz. 42 (1935), 11-44. Zbl0011.14802
  13. [13] R. Obláth, Note on the binomial coefficients, J. London Math. Soc. 23 (1948), 252-253. Zbl0033.24903
  14. [14] P. Ribenboim, The Little Book of Big Primes, Springer, 1991. Zbl0734.11001
  15. [15] N. Terai, On a Diophantine equation of Erdős, Proc. Japan Acad. Ser. A 70 (1994), 213-217. Zbl0821.11022
  16. [16] R. Tijdeman, Applications of the Gelfond-Baker method to rational number theory, in: Topics in Number Theory, North-Holland, 1976, 399-416. 

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