关于不等式S(x_1+x_2+…+x_t)<(1/t)(S(x_1)+S(x_2)+…+S(x_t))

On The Inequality S(x_1+x_2+…+x_t)<(1/t)(S(x_1)+S(x_2)+…+S(x_1))

对于正整数n,设S(n)是n的Sm arandache函数,笔者证明了:对于任何大于1的正整数t,不等式S(x1+x2+…+xt)<(S(x1)+S(x2)+…+S(xt))/t有无穷多组正整数解(x1,x2,…,xt).

For any positive integer n , let S（n） denote the Smarandache function ofn. The author proves that the inequality S（X1＋X2＋……Xt）〈 1/t （S（X1）＋S（X2）＋……S（Xt））/t has infinitely many positive integer solutions S（X1, X2,……, Xt） when any fixed positive integer t with t 〉 1.