| 摘要: |
| 针对Euler函数φ(n)与函数ω(n)混合的形如φ(n)=2ω(n)qω(n)1qω(n)2…qω(n)k的方程的可解性，其中q1,q2,…,qk为互异的奇素数，提出了方程φ(n)=2ω(n)5ω(n)的可解问题，利用Euler函数φ(n)与函数ω(n)的有关性质以及初等方法，得到了该方程的全部13组整数解n=1, 11, 202, 250, 2 222, 2 510, 2 750, 3 012, 3 750, 27 610, 37 650, 41 250, 414 150. |
| 关键词: 欧拉函数φ(n) 函数ω(n) 正整数解 |
| DOI： |
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| The Solutions of an Equation Involving Euler on Function φ(n) and Function ω(n) |
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AKIM Yoldax, MAMANTIMIN Adbikirim
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School of Mathematics and Statistics,Xinjiang Kashi University, Xinjiang Kashi 844008, China
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| Abstract: |
| Aiming at the solvability of the equation ω〖DD(-2mm〗—〖DD)〗(n) = 2ω(n)qω(n)1qω(n)2…qω(n)k in which Euler function φ(n) and function ω(n) are mixed, where q1,q2,…,qk are distinct odd prime numbers, the solvable problem of the equation φ(n)=2ω(n)5ω(n)was put forward. By using the properties of Euler function and function ω(n), and by using the elementary methods, the all 13 positive integer solutions n=1, 11, 202, 250, 2 222, 2 510, 2 750, 3 012, 3 750, 27 610, 37 650, 41 250, 414 150 were obtained. |
| Key words: Euler functionφ(n) function ω(n) positive integer solution |
