Hardy-Ramanujan Journal |
If Δm,n denotes the quotient [um,vn]/(um,vn) of the lcm by the gcd, we obtain in this paper a lower bound for the greatest square-free factor Q[Δm,n] of Δm,n when uh=vh,m>n (and un≠0); this implies a lower bound for logQ[un] of the form C(logm)2(loglogm)−1, thereby improving on an earlier result of C. L. Stewart.