论文标题
算术部分导数
The Arithmetic Partial Derivative
论文作者
论文摘要
算术部分导数（相对于Prime $ p $）是来自整数的函数，它将$ P $发送至1并满足Leibniz规则。在本文中，我们证明了$ p $ - 亚法的估值最终是周期性的。我们还证明了确定整数何时具有整体抗体导数的标准。作为一个应用程序，我们表明有许多无限的整数，这些整数恰好是任何非负整数$ n $的$ n $积分反派衍生物。
The arithmetic partial derivative (with respect to a prime $p$) is a function from the set of integers that sends $p$ to 1 and satisfies the Leibniz rule. In this paper, we prove that the $p$-adic valuation of the sequence of higher order partial derivatives is eventually periodic. We also prove a criterion to determine when an integer has integral anti-partial derivatives. As an application, we show that there are infinitely many integers with exactly $n$ integral anti-partial derivatives for any nonnegative integer $n$.
