Journal of Jianghan University(Natural Science Edition) ›› 2016, Vol. 44 ›› Issue (4): 321-326.doi: 10.16389/j.cnki.cn42-1737/n.2016.04.006

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Solution of Arithmetic Function Equation φ2(n) =S(n8)

XU Hongxin , ZHAO Xiqing*, ZHANG Lixia   

  1. College of Mathematics and Computer Science , Yan′an University , Yan′an 716000 , Shannxi , China
  • Online:2016-08-28 Published:2016-09-06
  • Contact: ZHAO Xiqing

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Abstract: The solvability of equation φ2(n) =S(n8) was studied and the only positive integer solutions n =189, 243, 343,375, 378, 486, 500, 686, 750, 867, 1 156, 1 734 of the equation were proved with the property of φ2(n), φ(n),S(n) , the elementary number theory methods and the C++ programs.

Key words: generalized Euler function, Euler function, Smarandache function, positive integer solution

CLC Number: