On a conjecture of Graham

Author:

Sander J. W.

Abstract

Let a 1 > a 2 > > a n {a_1} > {a_2} > \cdots > {a_n} be a finite sequence of positive integers containing a prime power p d {p^d} with the property: a i p k a j {a_i} \ne {p^k}{a_j} for all i , j i,j and k > 0 k > 0 . Then max i , j a i / ( a i , a j ) n {\max _{i,j}}{a_i}/\left ( {{a_i},{a_j}} \right ) \geq n .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference10 articles.

1. On a problem of R. L. Graham;Boyle, R. D.;Acta Arith.,1977

2. On a conjecture of Graham concerning a sequence of integers;Chein, E. Z.;Canad. Math. Bull.,1978

3. Problems and results on combinatorial number theory;Erdős, P.,1973

4. R. L. Graham, Unsolved problem 5749, Amer. Math. Monthly 77 (1970), 775.

5. The proof of a conjecture of Graham for sequences containing primes;Klein, Rivka;Proc. Amer. Math. Soc.,1985

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. None of the Above;Unsolved Problems in Number Theory;2004

2. None of the Above;Unsolved Problems in Number Theory;1994

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