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My Paper
Die Anzahl an Orbits unter Multiplikation modulo eine Zahl
This paper (in German) proves—amongst other things—the following formula:
\newcommand{\ord}{\mathop{\text{ord}}} \ord_{p^k}(m) = \ord_{p}(m) \cdot p^{\max(0, k - k_0 + 1)}
work in progress on github
This paper investigates the formula from the previous paper more closely and derives inequalities for perfect numbers.