The solutions of a ternary linear equation relation to two arithmetical functions
Let n be a positive integer,the arithmetic function φ(n)is Euler function,and arithmetic function φe(n)is generalized Euler function,whereeis a positive integer.The solvability of linear equation φ(abc)=3φ2(a)+4φ2(b)+5φ2(c)was discussed,based on the properties of Euler function φ(n)and generalized Euler function φ2(n),the all 54 sets of positive integer solution of it were given by using the elementary method.
arithmetic function φ(n)arithmetic function φe(n)equationpositive integer solution