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关于求前n个自然数的等幂和sum from m=1 to n m~b的问题,虽然早已有不少研究,但由于组合数学的发展,它现在仍然吸引着数学工作者。陈景润和黎鉴愚在文献(?)中求出了幂指数从1到30的等幂和公式,但是这些公式计算比较复杂。本文利用积分方法,可以比较简单地得出等幂和公式。
Regarding the problem of finding the equal power sum sum from m=1 to n m~b of the first n natural numbers, although there has been much research already, it still attracts mathematicians because of the development of combinatorial mathematics. Chen Jingrun and Li Jianyu have obtained the equivalent power sum formula from 1 to 30 in the literature (?), but these formulas are more complicated to calculate. In this paper, using the integral method, the equal-power sum formula can be obtained simply.