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ArticleOriginal scientific text

Title

Perfect powers in products of terms in an arithmetical progression III

Authors 1, 2

Affiliations

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

Bibliography

  1. P. Erdős, Note on the product of consecutive integers (I), J. London Math. Soc. 14 (1939), 194-198.
  2. P. Erdős, On the product of consecutive integers III, Indag. Math. 17 (1955), 85-90.
  3. P. Erdős and J. Turk, Products of integers in short intervals, Acta Arith. 44 (1984), 147-174.
  4. J.-H. Evertse, On the equation axⁿ-byⁿ=c, Compositio Math. 47 (1982), 289-315.
  5. J.-H. Evertse and J. H. Silverman, Uniform bounds for the number of solutions to Yⁿ=f(X), Math. Proc. Cambridge Philos. Soc. 100 (1986), 237-248.
  6. T. N. Shorey, On gaps between numbers with a large prime factor II, Acta Arith. 25 (1974), 365-373.
  7. T. N. Shorey, Perfect powers in values of certain polynomials at integer points, Math. Proc. Cambridge Philos. Soc. 99 (1986), 195-207.
  8. T. N. Shorey, Perfect powers in products of integers from a block of consecutive integers, Acta Arith. 49 (1987), 71-79.
  9. T. N. Shorey, Some exponential diophantine equations, in: New Advances in Transcendence Theory, A. Baker (ed.), Cambridge University Press, 1988, 217-229.
  10. T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Tracts in Math. 87, Cambridge University Press, 1986.
  11. T. N. Shorey and R. Tijdeman, On the greatest prime factor of an arithmetical progression II, Acta Arith. 53 (1990), 499-504.
  12. T. N. Shorey and R. Tijdeman, Perfect powers in products of terms in an arithmetical progression, Compositio Math. 75 (1990), 307-344.
  13. T. N. Shorey and R. Tijdeman, On the greatest prime factor of an arithmetical progression III, in: Diophantine Approximation and Transcendental Numbers, Luminy 1990, Ph. Philippon (ed.), to appear.
Acta Arithmetica
1992/61/4
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Pages:
391-398
Main language of publication
English
Received
1991-10-08
Published
1992
Exact and natural sciences