The work of al-F~risi on amicable numbers begins with nine propositions of elementary number theory. The purpose of this article is to produce an English translation of these propositions and to provide a commentary on al-Ffirisi's methods. In particular we consider whether he proved, or attempted to prove the Fundamental Theorem of Arithmetic.
There are hints of unique factorisation in Greek arithmetic. Indeed, some commentators have seen the Fundamental Theorem of Arithmetic (FTA), that the natural numbers can be expressed as products of primes in a unique way, lurking in Euclid’s Elements (c. 300BC). What can be said with certainty is that the history of the FTA is strangely obscure. It is not too much of an exaggeration to say that the result passed from being unknown to being obvious without a proof passing through the head of any mathematician.
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