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arxiv: 1103.2298 · v1 · pith:KPDWMHXCnew · submitted 2011-03-11 · 🧮 math.NT

Giuga Numbers and the arithmetic derivative

classification 🧮 math.NT
keywords arithmeticderivativegiuganumbersalthoughbringscharacterizeconjecture
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We characterize Giuga Numbers as solutions to the equation $n'=an+1$, with $a \in \mathbb{N}$ and $n'$ being the arithmetic derivative. Although this fact does not refute Lava's conjecture, it brings doubts about its veracity.

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    Defines ports as pairs (R,c) and port fillings via the arithmetic derivative to separate inherited and primitive constructions of primary pseudoperfect numbers.