On an equation of Goormaghtigh

Yu. V. Nesterenko; T. N. Shorey

Acta Arithmetica (1998)

  • Volume: 83, Issue: 4, page 381-389
  • ISSN: 0065-1036

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Yu. V. Nesterenko, and T. N. Shorey. "On an equation of Goormaghtigh." Acta Arithmetica 83.4 (1998): 381-389. <http://eudml.org/doc/207129>.

@article{Yu1998,
author = {Yu. V. Nesterenko, T. N. Shorey},
journal = {Acta Arithmetica},
keywords = {higher degree diophantine equations; equation of Goormaghtigh; linear forms in logarithms},
language = {eng},
number = {4},
pages = {381-389},
title = {On an equation of Goormaghtigh},
url = {http://eudml.org/doc/207129},
volume = {83},
year = {1998},
}

TY - JOUR
AU - Yu. V. Nesterenko
AU - T. N. Shorey
TI - On an equation of Goormaghtigh
JO - Acta Arithmetica
PY - 1998
VL - 83
IS - 4
SP - 381
EP - 389
LA - eng
KW - higher degree diophantine equations; equation of Goormaghtigh; linear forms in logarithms
UR - http://eudml.org/doc/207129
ER -

References

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  1. [1] A. Baker and G. Wüstholz, Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62. Zbl0788.11026
  2. [2] R. Balasubramanian and T. N. Shorey, On the equation a ( x m - 1 ) / ( x - 1 ) = b ( y n - 1 ) / ( y - 1 ) , Math. Scand. 46 (1980), 177-182. Zbl0425.10020
  3. [3] H. Davenport, D. J. Lewis and A. Schinzel, Equations of the form f(x) = g(y), Quart. J. Math. Oxford Ser. (2) 12 (1961), 304-312. Zbl0121.28403
  4. [4] R. Goormaghtigh, L'Intermédiaire des Mathématiciens 24 (1917), 88. 
  5. [5] T. Nagell, The diophantine equation x ² + 7 = 2 n , Ark. Mat. 4 (1961), 185-187. Zbl0103.03001
  6. [6] S. Ramanujan, Question 464, J. Indian Math. Soc. 5 (1913), Collected Papers, Cambridge Univ. Press, 1927, 327. 
  7. [7] C. Runge, Ueber ganzzahlige Los̈ungen von Gleichungen zwischen zwei Veränderlichen, J. Reine Angew. Math. 100 (1887), 425-435. 
  8. [8] N. Saradha and T. N. Shorey, On the equation (x+1)...(x+k) = (y+1)...(y+mk), Indag. Math. (N.S.) 3 (1992), 79-90. Zbl0757.11011
  9. [9] T. N. Shorey, On the equation a ( x m - 1 ) / ( x - 1 ) = b ( y n - 1 ) / ( y - 1 ) (II), Hardy-Ramanujan J. 7 (1984), 1-10. Zbl0575.10011
  10. [10] T. N. Shorey, Integers with identical digits, Acta Arith. 53 (1989), 187-205. Zbl0693.10008
  11. [11] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Tracts in Math. 87, Cambridge Univ. Press, 1986. Zbl0606.10011
  12. [12] C. L. Siegel, Ueber einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1 (1929), 70 pp. Zbl56.0180.05

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