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On the positive integer solution of a ternary variable coefficient Euler function equation. (Chinese. English summary) Zbl 1463.11013

Summary: Let \(\varphi (n)\) be a Euler function, the positive integer solutions of a ternary variable coefficient Diophantine equation \(\varphi (abc)=3\varphi (a)+4\varphi (b)+5\varphi (c)\) are explored. By using elementary methods and techniques, the main conclusions are expounded completely, and a total of 40 groups of positive integer solutions are obtained after analysis and screening. The classification method used in this paper and the idea of selecting coefficients as special Pythagorean numbers provide a new idea for the study of the same type equations.

MSC:

11A25 Arithmetic functions; related numbers; inversion formulas
11D72 Diophantine equations in many variables
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