On the number of prime factors of a finite arithmetical progression

T. N. Shorey; R. Tijdeman

Acta Arithmetica (1992)

  • Volume: 61, Issue: 4, page 375-390
  • ISSN: 0065-1036

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T. N. Shorey, and R. Tijdeman. "On the number of prime factors of a finite arithmetical progression." Acta Arithmetica 61.4 (1992): 375-390. <http://eudml.org/doc/206473>.

@article{T1992,
author = {T. N. Shorey, R. Tijdeman},
journal = {Acta Arithmetica},
keywords = {primes in arithmetic progressions; number of distinct prime factors; lower bounds},
language = {eng},
number = {4},
pages = {375-390},
title = {On the number of prime factors of a finite arithmetical progression},
url = {http://eudml.org/doc/206473},
volume = {61},
year = {1992},
}

TY - JOUR
AU - T. N. Shorey
AU - R. Tijdeman
TI - On the number of prime factors of a finite arithmetical progression
JO - Acta Arithmetica
PY - 1992
VL - 61
IS - 4
SP - 375
EP - 390
LA - eng
KW - primes in arithmetic progressions; number of distinct prime factors; lower bounds
UR - http://eudml.org/doc/206473
ER -

References

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  1. [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. [2] A. Baker and H. M. Stark, On a fundamental inequality in number theory, Ann. of Math. 94 (1971), 190-199. Zbl0219.12009
  3. [3] K. Győry, Explicit upper bounds for the solutions of some diophantine equations, Ann. Acad. Sci. Fenn. Ser. AI 5 (1980), 3-12. Zbl0402.10018
  4. [4] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford University Press, 1988. Zbl0020.29201
  5. [5] P. Moree, On arithmetical progressions having few different prime factors in comparison with their lengths, to appear. Zbl0821.11044
  6. [6] G. Pólya, Zur arithmetischen Untersuchung der Polynome, Math. Z. 1 (1918), 143-148. 
  7. [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. Zbl0297.10031
  8. [8] T. N. Shorey and R. Tijdeman, On the number of prime factors of an arithmetical progression, J. Sichuan Univ. 26 (1990), 72-74. Zbl0709.11004
  9. [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. Zbl0709.11004
  10. [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. [11] K. Yu, Linear forms in the p-adic logarithms, Acta Arith. 53 (1989), 107-186. Zbl0699.10050

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