lcm(1,2,...,n)
Source: Romania TST 1995
September 28, 2009
number theory unsolvednumber theory
Problem Statement
For each positive integer ,define f(n)\equal{}lcm(1,2,...,n).
(a)Prove that for every there exist consecutive positive integers on which is constant.
(b)Find the maximum possible cardinality of a set of consecutive positive integers on which is strictly increasing and find all sets for which this maximum is attained.