主要研究方程Z2（n）＋1=S（n）的可解性，利用初等方法以及Smarandache函数的性质，证明了该方程有无穷多个正整数解，并获得了所有正整数解的具体表现形式．%The main purpose of this paper is to study the solvability of the equation Z2（n） ＋ 1 = S（n）, and give its all positive integer solutions. The elementary method and the properties of Smarandache function have been used to prove that the equation has infinite positive integer solutions, and give the exact expressions of all positive integer solutions for the equation.
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