On the greatest prime factors of polynomials at integer points

T. N. Shorey; R. Tijdeman

Compositio Mathematica (1976)

  • Volume: 33, Issue: 2, page 187-195
  • ISSN: 0010-437X

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Shorey, T. N., and Tijdeman, R.. "On the greatest prime factors of polynomials at integer points." Compositio Mathematica 33.2 (1976): 187-195. <http://eudml.org/doc/89305>.

@article{Shorey1976,
author = {Shorey, T. N., Tijdeman, R.},
journal = {Compositio Mathematica},
language = {eng},
number = {2},
pages = {187-195},
publisher = {Noordhoff International Publishing},
title = {On the greatest prime factors of polynomials at integer points},
url = {http://eudml.org/doc/89305},
volume = {33},
year = {1976},
}

TY - JOUR
AU - Shorey, T. N.
AU - Tijdeman, R.
TI - On the greatest prime factors of polynomials at integer points
JO - Compositio Mathematica
PY - 1976
PB - Noordhoff International Publishing
VL - 33
IS - 2
SP - 187
EP - 195
LA - eng
UR - http://eudml.org/doc/89305
ER -

References

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  1. [1] A. Baker: Transcendental Number Theory, Cambridge University Press (1975). Zbl0297.10013MR422171
  2. [2] P. Erdös: On the greatest prime factor of Πxk=1 f(k). J. London Math. Soc.27 (1952) 379-384. Zbl0046.04102
  3. [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.). Zbl0296.10021MR419381
  4. [4] M. Keates: On the greatest prime factor of a polynomial. Proc. Edinb. Math. Soc. (2) 16 (1969) 301-303. Zbl0188.10201MR257034
  5. [5] S.V. Kotov: Greatest prime factor of a polynomial. Mat. Zametki13 (1973) 515-522; Math. Notes13 (1973) 313-317. Zbl0267.12002MR327670
  6. [6] M. Langevin: Plus grand facteur premier d'entiers consecutifs. C. R. Acad. Sc. Paris280A (1975) 1567-1570. Zbl0305.10041MR379403
  7. [7] K. Ramachandra and T.N. Shorey: On gaps between numbers with a large prime factor. Acta Arith.24 (1973) 99-111. Zbl0258.10022MR327684
  8. [8] A. Schinzel: On two theorems of Gelfond and some of their applications. Acta Arith.13 (1967) 177-236. Zbl0159.07101MR222034
  9. [9] A. Schinzel and R. Tijdeman: On the equation ym = P(x ). (To appear in Acta Arith.). Zbl0303.10016MR422150
  10. [10] T.N. Shorey: On gaps between numbers with a large prime factor II. Acta Arith.25 (1974) 365-373. Zbl0258.10023MR344201
  11. [11] T.N. Shorey: On linear forms in the logarithms of algebraic numbers. (To appear in Acta Arith.). Zbl0289.10023MR412117
  12. [12] C.L. Siegel: Approximation algebraischer Zahlen. Math. Z.10 (1921) 173-213. Zbl48.0163.07MR1544471JFM48.0163.07
  13. [13] V.G. Sprindžuk: The greatest prime divisor of a binary form. Dokl. Akad. Nauk BSSR15 (1971) 389-391. MR286752
  14. [14] R. Tijdeman: On integers with many small prime factors. Compositio Math.26 (1973) 319-330. Zbl0267.10056MR325549
  15. [15] C. Hooley: On the greatest prime factor of quadratic polynomials, Acta Math.117 (1976) 281-299. Zbl0146.05704MR204383

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