Abstract

A Leibniz-like function \(\chi \) is an arithmetic function (i.e., \(\chi : \mathbb {N}\rightarrow \mathbb {N}\)) satisfying the product rule (which is also known as “Leibniz’s rule”): \(\chi (MN) = \chi (M) \cdot N + M \cdot \chi (N)\). In this paper we study the computational power of efficient algorithms that are given oracle access to such functions. Among the results, we show that certain families of Leibniz-like functions can be use to factor integers, while many other families can used to compute the radicals of integers and other number-theoretic functions which are believed to be as hard as integer factorization [1, 2].

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