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arXiv · 1512.06401

Deterministic factorization of sums and differences of powers

Markus Hittmeir
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Abstract

Let $a,b\in \mathbb{N}$ be fixed and coprime such that $a>b$, and let $N$ be any number of the form $a^n\pm b^n$, $n\in\mathbb{N}$. We will generalize a result of Bostan, Gaudry and Schost and prove that we may compute the prime factorization of $N$ in \[ \mathcal{O}(\text{M}_{\text{int}}(N^{1/4}\sqrt{\log N})), \] $\text{M}_{\text{int}}(k)$ denoting the cost for multiplying two $k$-bit integers. This result is better than the currently best known general bound for the runtime complexity for deterministic integer factorization.

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Markus Hittmeir. 2015-12-20. Deterministic factorization of sums and differences of powers. https://doi.org/10.1090/mcom%2F3197

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