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

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 · eudml:205478
[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
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[9] A. Schinzel and R. Tijdeman : On the equation ym = P(x ) . (To appear in Acta Arith.). · Zbl 0303.10016 · eudml:205503
[10] T.N. Shorey : On gaps between numbers with a large prime factor II . Acta Arith. 25 (1974) 365-373. · Zbl 0258.10023 · eudml:205281
[11] T.N. Shorey : On linear forms in the logarithms of algebraic numbers . (To appear in Acta Arith.). · Zbl 0289.10023 · eudml:205457
[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 · numdam:CM_1973__26_3_319_0 · eudml:89173
[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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