Montgomery, Grant A2020-05-112020-05-112020https://hdl.handle.net/11299/213284Mathematics, Swenson College of Science and EngineeringA number n is said to have the constant-sum property if for every possible partition of n, there exists disjoint subsets of the first n integers, such that the sum of the elements in each subset have the same remainder when divided by n (This means they are congruent with some constant integer c modulo n). For the case when n is odd, Kaplan, Lev, and Roditty [1] proved in 2009 that there exists a constant-sum partition for n if and only if only there exists no more than one singleton set. For the case when n is even and split into an odd number of subsets, Freyberg [2] proved in 2019 that an n/2-sum partition exists for n if and only if there exists no more than one singleton subset. This leaves open the case when n is even and each subset has an even number of elements. My UROP project focused on the case when n is even and broken into groups that each have even cardinality, that is, they each have an even number of elements.enUniversity of Minnesota DuluthUndergraduate Research Opportunities ProgramSwenson College of Science and EngineeringDepartment of Mathematics and StatisticsScholarly Text or Essay