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arXiv · 1108.4762

Investigations on the properties of the arithmetic derivative

Niklas Dahl·Jonas Olsson·Alexander Loiko
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Abstract

We investigate the properties of arithmetic differentiation, an attempt to adapt the notion of differentiation to the integers by preserving the Leibniz rule, (ab)' = a'b + ab'. This has proved to be a very rich topic with many different aspects and implications to other fields of mathematics and specifically to various unproven conjectures in additive prime number theory. Our paper consists of a self-contaited introduction to the topic, along with a couple of new theorems, several of them related to arithmetic differentiation of rational numbers, a topic almost unexplored until now.

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Niklas Dahl, Jonas Olsson, Alexander Loiko. 2011-08-24. Investigations on the properties of the arithmetic derivative. https://arxiv.org/abs/1108.4762

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