# On the number of prime factors of a finite arithmetical progression

Acta Arithmetica (1992)

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

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topT. 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

top- [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. Zbl0219.12009
- [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] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford University Press, 1988. Zbl0020.29201
- [5] P. Moree, On arithmetical progressions having few different prime factors in comparison with their lengths, to appear. Zbl0821.11044
- [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. Zbl0297.10031
- [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] 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] 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. Zbl0699.10050

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