2021 OIM Problems/Problem 1
Problem
Let be a set of 10 different prime numbers and let be the set of all integers greater than 1 such that their prime factorizations contain only primes in . Each element in is colored in the following way:
a) each element in has a distinct color,
b) if , then has the same color as or ,
c) for each pair of distinct colors and , there are no (not necessarily distinct), with colored and , colored , such that both divides and divides . Show that there is some prime in such that all of its multiples in have the same color.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.