We have already seen in Chapter 8 (Proposition 8.1) that every integer greaterthan 1 is equal to a product of prime numbers; that is, it has a prime factoriza-tion. The main result of this chapter, the Fundamental Theorem of Arithmetic,tells us that this prime factorization is unique — in other words, there is es-sentially only one way of writing an integer as a product of primes. (In caseyou think this is somehow obvious, have a look at Exercise 6 at the end of thechapter to find an example of a number system where prime factorization isnot unique.)The Fundamental Theorem of Arithmetic may not seem terribly thrilling toyou at first sight. However, it is in fact one of the most important properties ofthe integers and has many consequences. I will endeavour to thrill you a littleby giving a few such consequences after we have proved the theorem.