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On the maximal length of two sequences of consecutive integers with the same prime divisors

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References

  1. A. Baker,The theory of linear forms in logarithms, Transcendence theory: Advances and applications, Academic Press (London and New York, 1977), 1–27.

    Google Scholar 

  2. P. Erdös, On the product of consecutive integers, 111,Indag. Math.,17 (1955), 85–90.

    Google Scholar 

  3. P. Erdös, How many pairs of products of consecutive integers have the same prime factors,Amer. Math. Monthly,87 (1980), 391–392.

    Google Scholar 

  4. P. Erdös and T. N. Shorey, On the greatest prime factor of 2p−1 for a primep and other expressions,Acta. Arith.,30 (1976), 257–265.

    Google Scholar 

  5. P. Erdös and J. Turk, Products of integers in short intervals,Acta Arith.,44 (1984), 147–174.

    Google Scholar 

  6. R. Guy,Unsolved Problems in Number Theory, Springer-Verlag (New York-Heidelberg-Berlin, 1981), B 19, p. 42 and B 35, p. 50.

    Google Scholar 

  7. H. Iwaniec and J. Pintz, Primes in short intervals,Mh. Math.,98 (1984), 115–143.

    Article  Google Scholar 

  8. S. Lang,Elliptic Curves Diophantine Analysis, Springer-Verlag (New York, Heidelberg and Berlin, 1978).

    Google Scholar 

  9. D. H. Lehmer, On a problem of Störmer,Illinois Jour. Math.,8, (1964), 57–79.

    Google Scholar 

  10. D. Richard,Définissabilité en arithmétique et méthode de codage ZBV appliquée à des langages avec successeur et coprimarité, Thèse (Lyon, 1985).

  11. D. Richard, Les relations arithmétiques sur les entiers primaires sont définissables au premier ordre par successeur et coprimarité,C. R. Acad. Sc. Paris, Sér. I,299 (1984), 795–798.

    Google Scholar 

  12. T. N. Shorey, On linear forms in the logarithms of algebraic numbers,Acta Arith.,30 (1976), 27–42.

    Google Scholar 

  13. T. N. Shorey and R. Tijdeman, On the greatest prime factors of polynomials at integer points,Compositio Math.,33 (1976), 187–195.

    Google Scholar 

  14. R. Tijdeman, On integers with many small prime factors,Compositio Math.,26 (1973), 319–330.

    Google Scholar 

  15. M. Waldschmidt, A lower bound for linear forms in logarithms,Acta Arith. 37 (1980), 257–283.

    Google Scholar 

  16. A. Woods,Some problems in logic and number theory, and their connections, Thesis (Manchester, 1981).

Download references

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Balasubramanian, R., Shorey, T.N. & Waldschmidt, M. On the maximal length of two sequences of consecutive integers with the same prime divisors. Acta Math Hung 54, 225–236 (1989). https://doi.org/10.1007/BF01952052

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