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August 7, 2025Open Access

On the factorization of iterates of xᵈ+c in large degree

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Key Points

Factorization of $f_{d,c}^n(x)-α$ is limited to $d$ in $K[x]$, showing deep connections to algebraic structures.
Proven cases exist for $d$, implying positive asymptotic density of certain polynomial degrees under specific conditions for $c$.
Density computations for prime divisors stem from the findings, linking polynomial behavior to orbit properties in number fields.
Finiteness of integral points is established for backward orbits, revealing constraints on polynomial properties over function fields.

Implication

This study demonstrates that factorization of iterations in polynomial forms limits results, indicating the influence of the abc conjecture.

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Cite This Study

Wade Hindes (2025) studied this question.

synapsesocial.com/papers/68e7f0af2d7e30942762caa4 https://doi.org/10.48550/arxiv.2508.05795

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