Abstract
Summary We survey the history of the arithmetic derivative and more recent advances in research on this topic. Among other things, we discuss a few generalizations of the original arithmetic derivative and some arithmetic differential equations that are related to Goldbach’s conjecture and the twin prime conjecture. Our primary purpose is to give an overview of this field, but we also aim at providing supplementary material for an introductory course on discrete mathematics or number theory. Therefore, our survey contains ten exercises.
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