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ArticleOriginal scientific text

Title

On arithmetic progressions with equal products

Authors 1, 1, 2

Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
  2. Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands

Bibliography

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  2. B. Brindza, On S-integral solutions of the equation ym=f(x), Acta Math. Hungar. 44 (1984), 133-139.
  3. J. W. S. Cassels, Factorization of polynomials in several variables, in: Proc. 15th Scandinavian Congress, Oslo 1968, Lecture Notes in Math. 118, Springer, 1970, 1-17.
  4. A. Ehrenfeucht, A criterion for absolute irreducibility of polynomials, Prace Mat. 2 (1958), 167-169 (in Polish).
  5. R. A. MacLeod and I. Barrodale, On equal products of consecutive integers, Canad. Math. Bull. 13 (1970), 255-259.
  6. L. J. Mordell, On the integer solutions of y(y+1) = x(x+1)(x+2), Pacific J. Math. 13 (1963), 1347-1351.
  7. T. J. Rivlin, The Chebyshev Polynomials, Wiley, New York, 1974.
  8. 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.
  9. N. Saradha and T. N. Shorey, On the equation (x+1)...(x+k) = (y+1)...(y+mk) with m = 3,4, Indag. Math. 2 (1991), 489-510.
  10. N. Saradha and T. N. Shorey, On the equation (x+1)...(x+k) = (y+1)...(y+mk), Indag. Math. 3 (1992), 79-90.
  11. N. Saradha and T. N. Shorey, On the equation x(x+d)...(x+(k-1)d) = y(y+d)...(y+(mk-1)d), Indag. Math. 3 (1992), 237-242.
  12. 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).
  13. N. Saradha, T. N. Shorey and R. Tijdeman, On arithmetic progressions of equal lengths with equal products, Math. Proc. Cambridge Philos. Soc., to appear.
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  15. T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, 1986.
Acta Arithmetica
1994/68/1
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Pages:
89-100
Main language of publication
English
Received
1994-03-23
Published
1994
Exact and natural sciences