Section 11.5 is about relatively prime integers.
Two integers a and b, not both 0, are called relatively prime if gcd(a,b)=1.
Section 11.6 is about The fundamental theorem of arithmetic.
Every integer > 2 is either prime or can be expressed as a product of primes; that is n=p1p2...pm , where p1,p2,...pm are primes. Furthermore, this factorization is unique except possibly for the order in which the factors occur.
The difficulty for this sections is that there are so many new theorems and corollaries to remember. That is difficult to keep them all straight and to not get confused about them. Reading through them is okay, but I fear in my ability to be able to use them effectively later on. I will need more practice with both of these sections in order to be efficient. Sometimes it is difficult to read over the proofs, and I feel like that happened to me in this chapter as well...
What I enjoyed about these sections is the new material. It is neat learning this stuff and seeing how it can be used in such simple ways to prove such complex things. Maybe it is not that way actually, but it sure feels like that to me. I really enjoyed reading over corollary 11.18 which says Every integer exceeding 1 has a prime factor. I know this to be true, but it's cool to see it proved later on with the lemma and the following proof.
-nap
Two integers a and b, not both 0, are called relatively prime if gcd(a,b)=1.
Section 11.6 is about The fundamental theorem of arithmetic.
Every integer > 2 is either prime or can be expressed as a product of primes; that is n=p1p2...pm , where p1,p2,...pm are primes. Furthermore, this factorization is unique except possibly for the order in which the factors occur.
The difficulty for this sections is that there are so many new theorems and corollaries to remember. That is difficult to keep them all straight and to not get confused about them. Reading through them is okay, but I fear in my ability to be able to use them effectively later on. I will need more practice with both of these sections in order to be efficient. Sometimes it is difficult to read over the proofs, and I feel like that happened to me in this chapter as well...
What I enjoyed about these sections is the new material. It is neat learning this stuff and seeing how it can be used in such simple ways to prove such complex things. Maybe it is not that way actually, but it sure feels like that to me. I really enjoyed reading over corollary 11.18 which says Every integer exceeding 1 has a prime factor. I know this to be true, but it's cool to see it proved later on with the lemma and the following proof.
-nap
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