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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The proof of a conjecture of Graham for sequences containing primes


Author: Rivka Klein
Journal: Proc. Amer. Math. Soc. 95 (1985), 189-190
MSC: Primary 11A05
MathSciNet review: 801321
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Abstract: Let $ {a_1} < {a_2} < \cdots < {a_n}$ be a finite sequence of positive integers. R. L. Graham has conjectured that $ {\max _{i,j}}\left\{ {{a_i}/({a_i},{a_j})} \right\} \geqslant n$. We verify this conjecture in case at least one of the $ {\alpha _i}$'s is prime.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0801321-2
PII: S 0002-9939(1985)0801321-2
Article copyright: © Copyright 1985 American Mathematical Society