On integers with many small prime factors

R. Tijdeman

Compositio Mathematica (1973)

  • Volume: 26, Issue: 3, page 319-330
  • ISSN: 0010-437X

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Tijdeman, R.. "On integers with many small prime factors." Compositio Mathematica 26.3 (1973): 319-330. <http://eudml.org/doc/89173>.

@article{Tijdeman1973,
author = {Tijdeman, R.},
journal = {Compositio Mathematica},
language = {eng},
number = {3},
pages = {319-330},
publisher = {Noordhoff International Publishing},
title = {On integers with many small prime factors},
url = {http://eudml.org/doc/89173},
volume = {26},
year = {1973},
}

TY - JOUR
AU - Tijdeman, R.
TI - On integers with many small prime factors
JO - Compositio Mathematica
PY - 1973
PB - Noordhoff International Publishing
VL - 26
IS - 3
SP - 319
EP - 330
LA - eng
UR - http://eudml.org/doc/89173
ER -

References

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  2. A. Baker [2] Contributions to the theory of diophantine equations: II. The diophantine equation y2 = x3+k. Phil. Trans. Royal Soc. (London), A263 (1968), 193-208. Zbl0157.09801
  3. A. Baker [3] A sharpening of the bounds for linear forms in logarithms II, to appear in the Siegel birthday volume of Acta Arith. Zbl0261.10025
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  7. P. Erdös [7] Some recent advances and current problems in number theory, Lectures on Modern Mathematics, Vol. III, 196-244, Wiley, New York, 1965. Zbl0132.28402MR177933
  8. P. Erdös and J.L. Selfridge [8 ] Some problems on the prime factors of consecutive integers II, Proc. Washington State Univ. Conf. Number Theory, Pullman (Wash.), 1971. Zbl0228.10028MR318076
  9. N.I. Fel'dman [9] Improved estimate for a linear form of the logarithms of algebraic numbers, Mat. Sb., 77 (1968), 432-436. Transl. Math. USSR Sb., 6 (1968), 393-406. Zbl0235.10018MR232736
  10. D. Hanson [10] On the product of the primes, Canad. Math. Bull., 15 (1972), 33-37. Zbl0231.10008MR313179
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  12. D.H. Lehmer [12] The prime factors of consecutive integers, Amer. Math. Monthly, 72 (1965) no. 2, part II, 19-20. Zbl0128.04002MR171739
  13. K. Mahler [13] Zur Approximation algebraischer Zahlen, Math. Ann., I: 107 (1933), 691-730, II: 108 (1933), 37-55. Zbl0006.15604JFM59.0220.01
  14. K. Mahler [14] Lectures on diophantine approximations. Part 1: g-adic numbers and Roth's theorem. Univ. of Notre Dame Press, Ind., 1961. Zbl0158.29903MR142509
  15. G. Pólya [15] Zur arithmetischen Untersuchung der Polynome, Math. Z., 1 (1918), 143-148. MR1544288JFM46.0240.04
  16. K. Ramachandra [16] A note on numbers with a large prime factor II, J. Indian Math. Soc., 34 (1970), 39-48. Zbl0218.10057MR299568
  17. J. Barkley Rosser and L. Schoenfeld [17] Approximate formulas for some functions of prime numbers, Illinois J. Math., 6 (1962), 64-94. Zbl0122.05001MR137689
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Citations in EuDML Documents

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  1. R. Tijdeman, On the maximal distance between integers composed of small primes
  2. R. Tijdeman, H. G. Meijer, On integers generated by a finite number of fixed primes
  3. H. G. Meijer, R. Tijdeman, On additive functions
  4. T. N. Shorey, R. Tijdeman, On the greatest prime factors of polynomials at integer points
  5. Michel Langevin, Quelques applications de nouveaux résultats de van der Poorten
  6. T. N. Shorey, Some applications of linear forms in logarithms
  7. Michel Langevin, Sur la fonction plus grand facteur premier
  8. Adolf Hildebrand, Gerald Tenenbaum, Integers without large prime factors

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