For every pair of positive integers (n,m) with n<m, denote s(n,m) be the number of positive integers such that the number is in the range [n,m] and the number is coprime with m. Find all positive integers m≥2 such that m satisfy these condition:
i) m−ns(n,m)≥ms(1,m) for all n=1,2,...,m−1;
ii) 2022m+1 is divisible by m2 vmonumber theoryDivisibility