摘要
设n是一正整数,讨论了广义Euler函数方程φ_6(n)=2~(ω(n))的可解性,基于初等方法获得了其所有的16个解.
Let n be a positive integer.The solvability of the equation φ_6(n)=2~(ω(n)) on generalized Euler function is studied in this paper,and the all its 16 solutions are obtained based on the elementary method.
引文
[1]CAI T X,SHEN Z Y,HU M J.On the Parity of the Generalized Euler Function[J].Advances in Mathematics,2013,42(4):505-510.
[2]俞洪玲,沈忠燕.与广义欧拉函数有关的方程[J].浙江外国语学院学报,2012(3):91-97.
[3]金明艳,沈忠燕.方程φ2(n)=2Ω(n)和φ2(φ2(n))=2Ω(n)的可解性[J].浙江外国语学院学报,2013(4):47-52.
[4]许宏鑫,赵西卿,张利霞.关于数论函数方程φ2(n)=S(n8)的解[J].江汉大学学报(自然科学版),2016,44(4):321-326.
[5]张利霞,赵西卿.一类包含伪Smarandache函数的方程[J].延安大学学报(自然科学版),2016,35(3):13-15.
[6]王容,廖群英.方程φe(n)=nd(e=1,2,4)的可解性[J].纯粹数学与应用数学,2016,32(5):481-494.
[7]SHEN Z Y,CAI T X,HU M J.On the Parity of the Generalized Euler Function(II)[J].Advances in Mathematics,2016,45(4):509-519.