A Practical Rule of Divisibility by 7 in Uqlīdisī's Kitab al-Fuşul fi al-Hisab al-Hindi

Abstract

There are many known examples of divisibility rules in modern mathematics. However, some of these rules are far from practical, such as the current divisibility rule by 7. A far more useful method can be found in the work of the tenth-century Islamic mathematician Abu al-H.asan al-Uql & imath;dis & imath; (d. 980), who proposed a divisibility rule for 7 in his treatise Kitab al-Fus.ul f & imath; al-H.isab al-Hind & imath;. Compared to modern techniques, Uql & imath;dis & imath;'s rule is both simpler and more practical. This article (re)introduces this rule, and provides an exposition of the mathematical reasoning that underpins it.