On a Conjecture of Graham Concerning Greatest Common Divisors
On a Conjecture of Graham Concerning Greatest Common Divisors
Let ${a_1} < {a_2} < \cdots < {a_n}$ be a finite sequence of positive integers. R. L. Graham has conjectured that ${\max _{i,j}}\{ {a_i}/({a_i},{a_j})\} \geqslant n$. The following are proved: (1) If ${a_l} = p$, a prime, for some l and $p \ne ({a_i} + {a_j})/2,1 \leqslant i < j …