ArticleOriginal scientific text

Title

On the number of prime factors of a finite arithmetical progression

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. A. Baker, The theory of linear forms in logarithms, in: Transcendence Theory: Advances and Applications, A. Baker and D. W. Masser (eds.), Academic Press, 1977, 1-27.
  2. A. Baker and H. M. Stark, On a fundamental inequality in number theory, Ann. of Math. 94 (1971), 190-199.
  3. K. Győry, Explicit upper bounds for the solutions of some diophantine equations, Ann. Acad. Sci. Fenn. Ser. AI 5 (1980), 3-12.
  4. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford University Press, 1988.
  5. P. Moree, On arithmetical progressions having few different prime factors in comparison with their lengths, to appear.
  6. G. Pólya, Zur arithmetischen Untersuchung der Polynome, Math. Z. 1 (1918), 143-148.
  7. K. Ramachandra, T. N. Shorey and R. Tijdeman, On Grimm's problem relating to factorisation of a block of consecutive integers, J. Reine Angew. Math. 273 (1975), 109-124.
  8. T. N. Shorey and R. Tijdeman, On the number of prime factors of an arithmetical progression, J. Sichuan Univ. 26 (1990), 72-74.
  9. 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.
  10. R. Tijdeman, On the product of the terms of a finite arithmetic progression, in: Proc. Conf. Diophantine Approximations and Transcendence Theory, RIMS Kokyuroku 708, Kyoto Univ., Kyoto 1989, 51-62.
  11. K. Yu, Linear forms in the p-adic logarithms, Acta Arith. 53 (1989), 107-186.
Pages:
375-390
Main language of publication
English
Received
1991-10-08
Published
1992
Exact and natural sciences