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Nilpotent polynomials over $\mathbb{Z}$

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For a polynomial $u(x)$ in $\mathbb{Z}[x]$ and $r\in\mathbb{Z}$, we consider the orbit of $u$ at $r$ denoted and defined by $\mathcal{O}_u(r):=\{u^{(n)}(r)~|~n\in\mathbb{N}\}$.
Sengupta, Sayak
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Nilpotent Elements in Rings of Integral Representations [PDF]

open access: yesProceedings of the American Mathematical Society, 1966
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