The set S={1,2,…,2022} is to be partitioned into n disjoint subsets S1,S2,…,Sn such that for each i∈{1,2,…,n}, exactly one of the following statements is true:(a) For all x,y∈Si, with x=y,gcd(x,y)>1.
(b) For all x,y∈Si, with x=y,gcd(x,y)=1.Find the smallest value of n for which this is possible. number theorycombinatorics