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Let K denote a field. A polynomial f(x)∈K[x] is said to bedecomposable over K if f(x)=g(h(x)) for somepolynomials g(x) and h(x)∈K[x] with 1<deg(h)<deg(f).Otherwise f(x) is called indecomposable. Iff(x)=g(xm) with m>1, then f(x) is said to betrivially decomposable. In this paper, we show that xd+ax+b isindecomposable and that if e denotes the largest proper divisorof d, then xd+ad−e−1xd−e−1+⋯+a1x+a0 is eitherindecomposable or trivially decomposable. We also show that ifgd(x,a) denotes the Dickson polynomial of degree d andparameter a and gd(x,a)=f(h(x)), then f(x)=gt(x−c,a) and h(x)=ge(x,a)+c

international journal of mathematics and mathematical sciences

On the decomposition of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$x^d + a^{e}x^e +\cdots + a_{1}x + a_0$"><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mi>d</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:msup><mml:mi>x</mml:mi><mml:mi>e</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:mo>⋯</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>a</…

On the decomposition ofxd+aexe+⋯+a1x+a