The solution of graham's greatest common divisor problem

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Abstract

The following conjecture of R. L. Graham is verified: If n≧n 0, where n 0 is an explicitly computable constant, then for any n distinct positive integers a 1, a 2, ..., a n we have {Mathematical expression} 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 of a i and a j .

Original languageEnglish (US)
Pages (from-to)67-71
Number of pages5
JournalCombinatorica
Volume6
Issue number1
DOIs
StatePublished - Mar 1 1986
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics

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