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arXiv · 1905.10704

Continued Fractions and Factoring

Michele Elia
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Abstract

Legendre found that the continued fraction expansion of $\sqrt N$ having odd period leads directly to an explicit representation of $N$ as the sum of two squares. Similarly, it is shown here that the continued fraction expansion of $\sqrt N$ having even period directly produces a factor of a composite $N$. Shanks' infrastructural method is then revisited, and some consequences of its application to factorization by means of the continued fraction expansion of $\sqrt N$ are derived.

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Michele Elia. 2019-05-26. Continued Fractions and Factoring. https://arxiv.org/abs/1905.10704

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