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On k-fold super totient numbers

    https://doi.org/10.1142/S179304212350032XCited by:0 (Source: Crossref)

    Let n be a positive integer and let R(n) be the set of positive integers less than n that are relatively prime to n. If R(n) can be partitioned into two subsets of equal sum, then n is called a super totient number. In this paper, we generalize this concept by considering when R(n) can be partitioned into k subsets of equal sum. Integers that admit such a partition are called k-fold super totient numbers. In this paper, we prove that for every odd positive integer k, there exists an integer Nk such that for all nNk, n is a k-fold super totient numbers provided that some trivial necessary condition is satisfied. Furthermore, we determine the smallest allowable values for N3 and N5.

    AMSC: 11A99, 11B99, 11P83
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