MathDB

2

Part of 2012 Canada National Olympiad

Problems(1)

L(n,k) is the lcm of k consecutive integers

Source: Canadian MO 2012

5/4/2012
For any positive integers nn and kk, let L(n,k)L(n,k) be the least common multiple of the kk consecutive integers n,n+1,…,n+k−1n,n+1,\ldots ,n+k-1. Show that for any integer bb, there exist integers nn and kk such that L(n,k)>bL(n+1,k)L(n,k)>bL(n+1,k).
number theoryleast common multiplenumber theory proposed