数论函数方程Z(n)=φ7(SL(n))的可解性
The Solvability of Arithmetic EquationZ(n)=φ7(SL(n))
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。
Abstract:
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.
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