On the decomposition of \(x^d + a_ex^e +\dots +a_1x +a_0\)
The author calls \(f(x)\in K[x]\) (for a field \(K\)) decomposable over \(K\) if \(f(x)= g(h(x))\) for some \(g(x),h(x)\in K[x]\) with \(1<\deg(h)< \deg(F)\) and indecomposable otherwise. Moreover, if \(f(x)= g(x^m)\) for \(m>1\), then \(f\) is called trivially decomposable. He shows that if \(e\) is the largest proper divisor of \(d\), then \(x^d+ a_{d-e-1}+ \cdots+ a_1x+a_0\) is either indecomposable or trivially decomposable. Results on Dickson polynomials are also presented.
scientific article; zbMATH DE number 1501978