The aim of this paper is to fill in the gaps in the formulation and the proof of a theorem contained in the paper by K.Ozeki (Aequ Math 25:247–252, 1982) published in this journal. We also give a short proof of this theorem and use it to obtain certain information about the factorization of polynomials of the form \(f(x)-f(y)\).

中文翻译：

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在函数方程 $$\varvec{f(\alpha x+\beta )=f(x)}$$ f ( α x + β ) = f ( x )

这篇论文的目的是填补 K.Ozeki (Aequ Math 25:247–252, 1982) 发表在该期刊上的论文中包含的定理的公式和证明中的空白。我们还给出了这个定理的简短证明，并使用它来获得有关\(f(x)-f(y)\)形式的多项式分解的某些信息。