The positive integer solutions of a five-variable Diophantine equation on Euler function
For any positive integer n,arithmetic function φ(n)is Euler function.The positive integer solutions of a five-variable Diophantine equationφ(x1x2x3x4x5)=3φ(x1)φ(x2)φ(x3)+4φ(x4)φ(x5)on Euler function φ(n)were discussed in this paper.By using the properties of Euler function φ(n)and the elementary method,the 501 positive integer solutions of this equation were obtained,and the 61 positive integer solutions satisfied x1≤x2≤x3 and x4≤x5 were given.
Euler function φ(n)Diophantine equationpositive integer solution
万方数据
维普
