On the polynomial equation $P(Q(x_1,\ldots,x_m))=Q(P(x_1),\ldots,P(x_m))$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910744869601280 |
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| author | Mingajev, Arseny |
| author_facet | Mingajev, Arseny |
| contents | We consider the equation $P(Q(x_1,\ldots,x_ν))=Q(P(x_1),\ldots,P(x_ν))$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the polynomial equation $P(Q(x_1,\ldots,x_m))=Q(P(x_1),\ldots,P(x_m))$ Mingajev, Arseny Number Theory Algebraic Geometry Rings and Algebras We consider the equation $P(Q(x_1,\ldots,x_ν))=Q(P(x_1),\ldots,P(x_ν))$ 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. |
| title | On the polynomial equation $P(Q(x_1,\ldots,x_m))=Q(P(x_1),\ldots,P(x_m))$ |
| topic | Number Theory Algebraic Geometry Rings and Algebras |
| url | https://arxiv.org/abs/2412.10465 |