List of thirty-three unsolved arithmetic problems of the time of Ibn Khawwām

Mathematicians have always been fascinated by the resolution of algebraic and Diophantine equations for which one seeks integer or rational solutions. We present a list of thirty-three open problems and conjectures in number theory, compiled and posed by the thirteenth-century Muslim mathematician — whose full name is ABDULLAH B. MUHAM-MAD B. MUHAMMAD AL-KHAWWĀM AL-BAGHDADI , better known as d’IBN AL-KHAWWAMM — in his arithmetic treatise al-Fawā’id al-Bahā’iya fi qawā’id al-Hisābiya. The list is presented here without commentary or solutions from our side.