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A Proof of Sondow’s Conjecture on the Smarandache Function
The American Mathematical Monthly ( IF 0.4 ) Pub Date : 2020-12-11 Xiumei Li, Min Sha
中文翻译:
关于Smarandache函数的Sondow猜想的证明
更新日期:2020-12-11
The American Mathematical Monthly ( IF 0.4 ) Pub Date : 2020-12-11 Xiumei Li, Min Sha
Abstract
The Smarandache function of a positive integer n, denoted by S(n), is defined to be the smallest positive integer j such that n divides the factorial . In this note, we prove that for any fixed number k > 1, the inequality holds for almost all positive integers n. This confirms Sondow’s conjecture which asserts that the inequality holds for almost all positive integers n.
中文翻译:
关于Smarandache函数的Sondow猜想的证明
摘要
将由S(n)表示的正整数n的Smarandache函数定义为最小的正整数j,以使n除以阶乘。在本说明中,我们证明了对于任何固定数k > 1,不等式几乎适用于所有正整数n。这证实了桑多的猜想,后者断定不平等几乎适用于所有正整数n。