ArticleOriginal scientific text

Title

On an equation of Goormaghtigh

Authors 1, 2

Affiliations

  1. Department of Mathematics, Moscow State University, Moscow 119899, Russia
  2. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India

Bibliography

  1. A. Baker and G. Wüstholz, Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62.
  2. R. Balasubramanian and T. N. Shorey, On the equation axm-1x-1=byn-1y-1, Math. Scand. 46 (1980), 177-182.
  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.
  4. R. Goormaghtigh, L'Intermédiaire des Mathématiciens 24 (1917), 88.
  5. T. Nagell, The diophantine equation x²+7=2n, Ark. Mat. 4 (1961), 185-187.
  6. S. Ramanujan, Question 464, J. Indian Math. Soc. 5 (1913), Collected Papers, Cambridge Univ. Press, 1927, 327.
  7. C. Runge, Ueber ganzzahlige Los̈ungen von Gleichungen zwischen zwei Veränderlichen, J. Reine Angew. Math. 100 (1887), 425-435.
  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.
  9. T. N. Shorey, On the equation axm-1x-1=byn-1y-1 (II), Hardy-Ramanujan J. 7 (1984), 1-10.
  10. T. N. Shorey, Integers with identical digits, Acta Arith. 53 (1989), 187-205.
  11. T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Tracts in Math. 87, Cambridge Univ. Press, 1986.
  12. C. L. Siegel, Ueber einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1 (1929), 70 pp.
Pages:
381-389
Main language of publication
English
Received
1997-03-24
Accepted
1997-09-22
Published
1998
Exact and natural sciences