| 摘要: |
| 令数论函数φ(n)为Euler函数，数论函数φe(n)为广义Euler函数,基于Euler函数φ(n)与广义Euler函数φe(n)混合的不定方程的可解性，提出了方程φ(ab)=11φ2(a)+13φ2(b)的整数解的求解问题，利用函数φ(n)与φ2(n)的有关性质，采用分类分段的讨论方式，得到了该方程有21组正整数解. |
| 关键词: 数论函数φ(n) 数论函数φe(n) 方程 正整数解 |
| DOI： |
| 分类号: |
| 基金项目: |
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| The Solvability of Arithmetic Function Equation φ(ab)=11φ2(a)+13φ2(b) |
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ZHENG Xin-xin, LIU Zhen
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| Abstract: |
| Let the arithmetic function φ(n) be Euler function, and let the arithmetic function φe(n) be generalized Euler function. Based on the solvability of the Diophantine equation mixed with the Euler function φ(n) and the generalized Euler functionφe(n), the issue of solving the integer solutions of the equation φ(ab)=11φ2(a)+13φ2(b) was proposed. By using the properties of the functionsφ(n) andφ2(n), and combination of classification and segmentation, the 21 positive integer solutions of the equation were obtained. |
| Key words: arithmetic function φ(n) arithmetic function φe(n) equation positive integer solution |
