摘要
研究数论函数的各种性质是初等数论的一个重要内容,而著名的Smarandache函数S(n)是重要的数论函数之一,它是由美籍罗马尼亚著名数论专家Florentin Smarandache教授首先提出的。许多学者对Smarandache函数的性质及含有Smarandache函数的方程的可解性做了深入的研究,并取得了丰硕的成果。文章证明了包含Smarandache函数的方程φ(n)=S(n10)的可解性,并给出了该方程的全部正整数解。
The research on various properties of arithmetical functions is one of the important elements in elementary number theory.The famous Smarandache function S(n) is one of the important arithmetical functions developed by professor Smarandache.The property of the function and the solvability of the equation involving Smarandache function have been researched by many scholars and achieved fruitful results.The solvability of φ(n)=S(n 10) was proved based on the interest of Smarandache function and all the positive integer solutions of the equation were provided as well.
