算术级数子集的最小公倍数

摘要

运用概率的方法研究了算术级数U的子集的最小公倍数。证明了对任意的0<θ<1,对几乎所有长度为[nθ]的U的子集A,都有loglcm{a：a∈A}=(1-θ)nθlogn+o(nθ)。%For a positive arithmetic progression U={u+d,u+2d,…,u+nd},( u,d)=1,we study the logarithm of the least common multiple of subsets of the set U. We show that for any 0<θ<1,loglcm{a:a∈A}=(1-θ)nθlogn+o(nθ) for almost all sets A⊂U of size [ nθ] .