An overview of Algorithms on Integer Calculation

This work proposes a new meta-mathematical method called arithmetic optimization algorithm that uses the distributive behavior of the main arithmetic operators in mathematics, including division, subtraction, and addition for now the number of distinct entries in the multiplication table n. Therefore, there is some interest in algorithms for calculating M (n) exactly or as an approximation. We compare several algorithms for exact calculation of M (n) and come up with a new algorithm with suborder execution time. We also present two Monte Carlo algorithms to approximate M (n). We give exact calculation results for values of n to 230 and compare our experimental results with Ford's order of magnitude results. Experimental results show that INTEGERS provides very promising results in solving difficult optimization problems compared to 11 other well-known optimization algorithms.