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Shorey, T. N.; Tijdeman, R.

On the greatest prime factors of polynomials at integer points. (English) Zbl 0338.10040

Compos. Math. 33, 187-195 (1976).
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Cited in 3 Documents

MathOverflow Questions:

Do consecutive integers have a big prime factor?

MSC:

11N05 Distribution of primes
11J81 Transcendence (general theory)
11A41 Primes
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References:

[1] A. Baker : Transcendental Number Theory , Cambridge University Press (1975). · Zbl 0297.10013
[2] P. Erdös : On the greatest prime factor of \Pi xk=1 f(k) . J. London Math. Soc. 27 (1952) 379-384. · Zbl 0046.04102 · doi:10.1112/jlms/s1-27.3.379
[3] P. Erdös and T.N. Shorey : On the greatest prime factor of 2p - 1 for a prime p and other expressions . (To appear in Acta Arith.). · Zbl 0296.10021
[4] M. Keates : On the greatest prime factor of a polynomial . Proc. Edinb. Math. Soc. (2) 16 (1969) 301-303. · Zbl 0188.10201 · doi:10.1017/S0013091500012967
[5] S.V. Kotov : Greatest prime factor of a polynomial . Mat. Zametki 13 (1973) 515-522; Math. Notes 13 (1973) 313-317. · Zbl 0267.12002 · doi:10.1007/BF01146565
[6] M. Langevin : Plus grand facteur premier d’entiers consecutifs . C. R. Acad. Sc. Paris 280A (1975) 1567-1570. · Zbl 0305.10041
[7] K. Ramachandra and T.N. Shorey : On gaps between numbers with a large prime factor . Acta Arith. 24 (1973) 99-111. · Zbl 0258.10022
[8] A. Schinzel : On two theorems of Gelfond and some of their applications . Acta Arith. 13 (1967) 177-236. · Zbl 0159.07101
[9] A. Schinzel and R. Tijdeman : On the equation ym = P(x ) . (To appear in Acta Arith.). · Zbl 0303.10016
[10] T.N. Shorey : On gaps between numbers with a large prime factor II . Acta Arith. 25 (1974) 365-373. · Zbl 0258.10023
[11] T.N. Shorey : On linear forms in the logarithms of algebraic numbers . (To appear in Acta Arith.). · Zbl 0289.10023
[12] C.L. Siegel : Approximation algebraischer Zahlen . Math. Z. 10 (1921) 173-213. · JFM 48.0163.07
[13] V.G. Sprindžuk : The greatest prime divisor of a binary form . Dokl. Akad. Nauk BSSR 15 (1971) 389-391.
[14] R. Tijdeman : On integers with many small prime factors . Compositio Math. 26 (1973) 319-330. · Zbl 0267.10056
[15] C. Hooley : On the greatest prime factor of quadratic polynomials , Acta Math. 117 (1976) 281-299. · Zbl 0146.05704 · doi:10.1007/BF02395047
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