In this paper, we introduce some new semiring structures by considering the prime factors, sum of divisors and the number of relatively prime positive divisors of a pair of non-negative integers and solve a variety of system of linear equations over one of these semirings. We then discuss the properties of these structures and how they compare with classical algebra. The paper is concluded by providing a key-exchange scheme using one of the newly discovered semirings.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.