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In this note, we briefly analyse the works on the extractions of amicablepairs in some medieval Arabic literature. In this note, we briefly analyse theworks Ibn Sina (c.980-1037), al-Baghdadi (c.980-1037) and al-Kashi (d. c. 1429)on the extraction of amicable pairs. We compare these works in the view of thewell-known Thabit ibn Qurra's rule. Contrary to the belief that these authorsare merely stating variations of the famous Thabit ibn Qurra's (d. 901) rule indifferent manners, we show that their statements are different. We prove thatthe statements of both ibn Sina and al-Baghdadi led to an unsolved conjecture,while al-Kashi's statement led to the wrong amicable pair (2024, 2296). Theconjecture implied by ibn Sina and al-Baghdadi statements requires testing bigprimes corresponding to the known 51 Mersenne primes, and we show that nocounterexamples yet exist.

On the Extraction of Amicable Pairs Between Ibn Sina-al-Baghdadi and al-Kashi