A CRITERION FOR POLYNOMIAL DECOMPOSITION - Lazov, Petar R. (Matematichki Bilten, 1995)
Abstract: Let \(B=B(x)\) be a complex polynomial for which \[ B(x)=m· n,m≥ 1,n≥ 2,m,nN. \] In this work we state a criterion for the following proposition to hold: \[ { aligned &there exist complex polynomials y=y(x),y(x)=m &and u=u(x),u(x)=n,such that &B(x)=u(y(x)). aligned . \] In addition, as an auxiliary result we obtain a theorem that completely solves the problem of the polynomial solutions of the algebraic equation \[ B(x)=c_0+c_1· y+…+c_n-1· y^n-1+c_n· y^n, \] giving also an algorithm for finding them.