Minorations non triviales du plus petit commun multiple de certaines suites finies d'entiers

In the last part of this Note, we study the integer lcm(n,n+1,…,n+k) (k∈N,n∈N∗). We show that it has a divisor dn,k simple in its dependence on n and k, and a multiple mn,k also simple in its dependence on n. In addition, we prove that both equalities: lcm(n,n+1,…,n+k)=dn,k and lcm(n,n+1,…,n+k)=mn,k hold for infinitely many pairs (n,k). To cite this article: B. Farhi, C. R. Acad. Sci. Paris, Ser. I 341 (2005).