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.
关键词
Euler函数/不定方程/正整数解
Key words
Euler function φ(n)/Diophantine equation/positive integer solution
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