min no of partitions of 1-100 , each group every 2 are coprime, or any 2 are not
Source: (2021 -) 2022 Dürer Math Competition Regional E4 E+1 https://artofproblemsolving.com/community/c1621671_
November 30, 2022
combinatoricsnumber theorycoprime
Problem Statement
We want to partition the integers into several groups such that within each group either any two numbers are coprime or any two are not coprime. At least how many groups are needed for such a partition?We call two integers coprime if they have no common divisor greater than .