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Discussion of solutions of an equation on the number-theoretic function \(\varphi(m)\). (Chinese. English summary) Zbl 1463.11107

Summary: Let \(\varphi(m)\) be an Euler function, where \(m\) is a positive integer. The solvability of the equation \(\varphi(xyz) = 7(\varphi(x) + \varphi(y) + \varphi(z))\) containing the Euler function \(\varphi(m)\) was discussed. By using elementary methods and the properties of the Euler function \(\varphi(m)\), all 87 sets of positive integer solutions of the equation were given.

MSC:

11D72 Diophantine equations in many variables
11D45 Counting solutions of Diophantine equations
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