On -fold super totient numbers
Abstract
Let be a positive integer and let be the set of positive integers less than that are relatively prime to . If can be partitioned into two subsets of equal sum, then is called a super totient number. In this paper, we generalize this concept by considering when can be partitioned into subsets of equal sum. Integers that admit such a partition are called -fold super totient numbers. In this paper, we prove that for every odd positive integer , there exists an integer such that for all , is a -fold super totient numbers provided that some trivial necessary condition is satisfied. Furthermore, we determine the smallest allowable values for and .
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