On k-fold super totient numbers
| Autor: | Joshua Harrington, Melea Roman, Andrew Vincent, Tony W. H. Wong |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | International Journal of Number Theory. 19:655-666 |
| ISSN: | 1793-7310 1793-0421 |
| DOI: | 10.1142/s179304212350032x |
| Popis: | Let [Formula: see text] be a positive integer and let [Formula: see text] be the set of positive integers less than [Formula: see text] that are relatively prime to [Formula: see text]. If [Formula: see text] can be partitioned into two subsets of equal sum, then [Formula: see text] is called a super totient number. In this paper, we generalize this concept by considering when [Formula: see text] can be partitioned into [Formula: see text] subsets of equal sum. Integers that admit such a partition are called [Formula: see text]-fold super totient numbers. In this paper, we prove that for every odd positive integer [Formula: see text], there exists an integer [Formula: see text] such that for all [Formula: see text], [Formula: see text] is a [Formula: see text]-fold super totient numbers provided that some trivial necessary condition is satisfied. Furthermore, we determine the smallest allowable values for [Formula: see text] and [Formula: see text]. |
| Databáze: | OpenAIRE |
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