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

 

On a conjecture of Graham


Author: J. W. Sander
Journal: Proc. Amer. Math. Soc. 102 (1988), 455-458
MSC: Primary 11A05
MathSciNet review: 928959
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Abstract: Let $ {a_1} < {a_2} < \cdots < {a_n}$ be a finite sequence of positive integers containing a prime power $ {p^d}$ with the property: $ {a_i} \ne {p^k}{a_j}$ for all $ i,j$ and $ k > 0$. Then $ {\max _{i,j}}{a_i}/\left( {{a_i},{a_j}} \right) \geq n$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0928959-9
PII: S 0002-9939(1988)0928959-9
Article copyright: © Copyright 1988 American Mathematical Society