A List of Open Problems in Number Theory Posed by Ibn al-Khawwām (13th Century): Historical and Arithmetic Analysis

K. I. A Derouiche

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arXiv · 2511.08400

A List of Open Problems in Number Theory Posed by Ibn al-Khawwām (13th Century): Historical and Arithmetic Analysis

K. I. A Derouiche

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Abstract

Mathematicians have long been fascinated by the resolution of algebraic and Diophantine equations in search of integer or rational solutions. This article presents a list of thirty-three open problems in number theory, posed in the 13th century by Ibn al-Khawwām al-Baghdādī (Abdallāh ibn Muhammad ibn Muhammad al-Khawwām), extracted from his arithmetic treatise al-Fawāid al-Bahāiyya fī qawāid al-hisābiyya. We provide a historical and arithmetic analysis of these problems and their solutions, and, whenever possible, offer original solutions and bibliographic notes. This work situates these problems within the broader development of number theory.

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K. I. A Derouiche. 2025-11-11. A List of Open Problems in Number Theory Posed by Ibn al-Khawwām (13th Century): Historical and Arithmetic Analysis. https://arxiv.org/abs/2511.08400

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