ArticleOriginal scientific text

Title

On the equation x(x+1)... (x+k-1) = y(y+d)... (y+(mk-1)d), m=1,2

Authors 1, 1, 2

Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India
  2. Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands

Bibliography

  1. A. Baker, Bounds for the solutions of the hyperelliptic equation, Proc. Cambridge Philos. Soc. 65 (1969), 439-444.
  2. L. E. Dickson, History of the Theory of Numbers, Vol. II, first publ. in 1919. Reprint: Chelsea, New York, 1971.
  3. Ya. Gabovich, On arithmetic progressions with equal products of terms, Colloq. Math. 15 (1966), 45-48 (in Russian).
  4. Problèmes P543 et P545, R1, Colloq. Math. 19 (1968), 179-180.
  5. N. Saradha and T. N. Shorey, On the ratio of two blocks of consecutive integers, Proc. Indian Acad. Sci. Math. Sci. 100 (1990), 107-132.
  6. N. Saradha and T. N. Shorey, On the equation x(x+d₁) ... (x + (k-1)d₁) = y(y+d₂) ... (y + (mk-1)d₂), Proc. Indian Acad. Sci. Math. Sci. 104 (1994), 1-12.
  7. N. Saradha, T. N. Shorey and R. Tijdeman, On arithmetic progressions of equal lengths with equal products, Math. Proc. Cambridge Philos. Soc., to appear.
  8. T. N. Shorey and R. Tijdeman, Perfect powers in products of terms in an arithmetical progression (II), Compositio Math. 82 (1992), 119-136.
Pages:
181-196
Main language of publication
English
Received
1994-10-26
Published
1995
Exact and natural sciences