On the polynomial equation $P(Q(x_1,\ldots,x_m))=Q(P(x_1),\ldots,P(x_m))$

Arseny Mingajev

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arXiv · 2412.10465

On the polynomial equation $P(Q(x_1,\ldots,x_m))=Q(P(x_1),\ldots,P(x_m))$

Arseny Mingajev

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Abstract

We consider the equation $P(Q(x_1,\ldots,x_\nu))=Q(P(x_1),\ldots,P(x_\nu))$ in polynomials over the field of complex numbers and prove that if ${\rm deg}(P)>1$, then it is only solvable in polynomials that are affinely conjugate to monomials.

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Arseny Mingajev. 2024-12-12. On the polynomial equation $P(Q(x_1,\ldots,x_m))=Q(P(x_1),\ldots,P(x_m))$. https://arxiv.org/abs/2412.10465

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