On the Limiting Distribution of the Number of Unitary Coprime Pairs of Random Integers

In this paper, we study the limiting distribution of pairs of integers satisfying certain unitary properties. We prove that, for a sufficiently large random sample of integers, the number of semi-unitary coprime pairs converges in distribution to a standard normal random variable, and we provide the rate of convergence. Moreover, we establish a similar result for the limiting distribution of unitary coprime pairs.