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Combinatorica

, Volume 6, Issue 1, pp 67–71 | Cite as

The solution of graham’s greatest common divisor problem

  • M. Szegedy
Article

Abstract

The following conjecture of R. L. Graham is verified: Ifnn 0, wheren 0 is an explicitly computable constant, then for anyn distinct positive integersa 1,a 2, ...,a n we have\(\mathop {\max }\limits_{i,j} \) a i /(a i ,a j ) ≧ ≧n, and equality holds only in two trivial cases. Here (a i ,a j ) stands for the greatest cnmmon divisor ofa i anda j .

AMS subject classification (1980)

10 A 05 10 A 25 

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References

  1. [1]
    P. Erdős andR. L. Graham,Old and New Problems and Results in Combinatorial Number Theory, Genève, 1980.Google Scholar
  2. [2]
    R. L. Graham, Unsolved problem 5749,Amer. Math. Monthly,77 (1970), 775.CrossRefGoogle Scholar
  3. [3]
    D. R. Heat-Brown andH. Iwaniec, On the difference between consecutive primes,Invent. Math. 55 (1979), 49–69.CrossRefMathSciNetGoogle Scholar

Copyright information

© Akadémiai Kiadó 1986

Authors and Affiliations

  • M. Szegedy
    • 1
  1. 1.Department of Algebra and Number TheoryInstitute of Mathematics, L. Eötvös UniversityBudapestHungary

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