数论函数方程Z(n)=φ7(SL(n))的可解性  

The Solvability of Arithmetic EquationZ(n)=φ7(SL(n))

作　　者：向万国 尹秘 王军 钟佐琴 

机构地区：[1]云南民族大学数学与计算机科学学院,云南 昆明

出　　处：《应用数学进展》2024年第6期2791-2801,共11页Advances in Applied Mathematics

摘　　要：本文主要研究数论函数方程Z(n)=φ7(SL(n))的可解性。为此,先给出广义欧拉函数φ7(n)的表达式。由此,给出φ7(pβ)的表达式,其中p是素数,且β∈ℤ+。最后,讨论该方程的可解性,我们证明了其无正整数解。In this paper, we mainly study the solvability of the arithmetic equationZ(n)=φ7(SL(n)). For this purpose, we derive the expression of the generalized Euler functionφ7(n), from which the formula ofφ7(pβ)is obtained, where p is prime, andβ∈ℤ+. Afterwards, the solvability of the above equation is discussed, thus drawing the conclusion that it is has no solution in positive integers.

关 键 词：欧拉函数 广义欧拉函数 可解性 整数解 

分 类 号：O15[理学—数学]