On the number of prime factors of a finite arithmetical progression

• Autorzy: T. N. Shorey , R. Tijdeman
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1992
• Tom: 61
• Numer: 4
• Strony: 375-390

Daty

wydano

1992

otrzymano

1991-10-08

Twórcy

autor

T. N. Shorey

• School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

autor

R. Tijdeman

• Mathematical Institute, R. U. Leiden, P.O. Box 9512, 2300 RA Leiden, the Netherlands

Bibliografia

• [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.