Continued Fractions and Factoring

zbMATH Open1475.11013arXiv1905.10704MaRDI QIDQ5149076

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Publication date: 6 February 2021

Abstract: Legendre found that the continued fraction expansion of $sqrtN$ 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 $sqrtN$ 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 $sqrtN$ are derived.

Full work available at URL: https://arxiv.org/abs/1905.10704

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