FTA Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic | by Maths and Musings | Cantor’s Paradise

https://www.cantorsparadise.com/the-fundamental-theorem-of-arithmetic-37470aa1a7a0

Note:

The Fundamental Theorem of Arithmetic (FTA):

2300 years ago Euclid 《Elements》proved prime factorisation :
If p | x. y then p | x or p |y

19CE Gauss proved FTA. Uniqueness of prime factorisation.

French 《Bezout Theorem》 is the useful tool: if p, q co-prime, then there exist n, m integers such that
np + mq = 1
eg. Prove 5, 7 co-prime,
(3) *5+ (-2) *7 = 15-14=1

Strange, why Bezout Theorem not taught in A level ?

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