Abstract
For any positive integer n, the famous Pseudo Smarandache function Z(n) is de¯ned as the smallest integer m such that n evenly divides Xm k=1 k. That is, Z(n) = min ½ m : nj m(m + 1) 2; m 2 N¾, where N denotes the set of all positive integers. The main purpose of this paper is using the elementary method to study the properties of the Pseudo Smarandache function Z(n), and solve two conjectures posed by Kenichiro Kashihara in ref- erence [2].
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