On the diophantine equation n ( n + 1 ) . . . ( n + k - 1 ) = b x l

K. Győry

Acta Arithmetica (1998)

  • Volume: 83, Issue: 1, page 87-92
  • ISSN: 0065-1036

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K. Győry. "On the diophantine equation $n(n+1)...(n+k-1) = bx^l$." Acta Arithmetica 83.1 (1998): 87-92. <http://eudml.org/doc/207107>.

@article{K1998,
author = {K. Győry},
journal = {Acta Arithmetica},
keywords = {exponential equation; product of consecutive positive integers; arithmetic progressions},
language = {eng},
number = {1},
pages = {87-92},
title = {On the diophantine equation $n(n+1)...(n+k-1) = bx^l$},
url = {http://eudml.org/doc/207107},
volume = {83},
year = {1998},
}

TY - JOUR
AU - K. Győry
TI - On the diophantine equation $n(n+1)...(n+k-1) = bx^l$
JO - Acta Arithmetica
PY - 1998
VL - 83
IS - 1
SP - 87
EP - 92
LA - eng
KW - exponential equation; product of consecutive positive integers; arithmetic progressions
UR - http://eudml.org/doc/207107
ER -

References

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  3. [3] P. Erdős, On a diophantine equation, ibid. 26 (1951), 176-178. Zbl0043.04309
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  8. [8] A. J. J. Meyl, Question 1194, Nouv. Ann. Math. (2) 17 (1878), 464-467. 
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  13. [13] T. N. Shorey, Some exponential diophantine equations, in: New Advances in Transcendence Theory, A. Baker (ed.), Cambridge Univ. Press, 1988, 352-365. 
  14. [14] T. N. Shorey, Perfect powers in products of arithmetical progressions with fixed initial term, Indag. Math. (N.S.) 7 (1996), 521-525. Zbl0874.11034
  15. [15] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Univ. Press, 1986. 
  16. [16] J. J. Sylvester, On arithmetic series, Messenger Math. 21 (1892), 1-19 and 87-120. 
  17. [17] R. Tijdeman, Diophantine equations and diophantine approximations, in: Number Theory and Applications, R. A. Mollin (ed.), Kluwer Acad. Publ., 1989, 215-243. Zbl0719.11014
  18. [18] R. Tijdeman, Exponential diophantine equations 1986-1996, in: Number Theory, K. Győry, A. Pethő and V. T. Sós (eds.), W. de Gruyter, to appear. Zbl0606.10011
  19. [19] G. N. Watson, The problem of the square pyramid, Messenger Math. 48 (1919), 1-22. 

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