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Chapter 1 The unique factorization theorem
We assume as known the positive integers 1,2,3,..., the negative integers -1,-2,-3,..., and zero, which we reckon as an integer. By the non-negative integers we mean the positive integers together with zero. We assume as known the elementary arithemetical operations on integers. An integer a is said to divisible by a nozero integer b, if there an integer c,such that a = bc. We then say that a is an integer multiple or just a multiple of b. An integer p, where p > 1 , is a prime number,or a prime, if its only positive divisors are 1 and p.
2 The unique factorization theorem
If n is an integer greater than 1,then n is a product of primes. The standard form of an integer n,which is greater than 1,is unique.