The solution of graham’s greatest common divisor problem


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 .

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Szegedy, M. The solution of graham’s greatest common divisor problem. Combinatorica 6, 67–71 (1986).

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AMS subject classification (1980)

  • 10 A 05
  • 10 A 25