My thoughts on the "relatively prime." My first observation was that we are trying to get the linear combination to add to one. This was unique to me because the definition of a prime is that its only factor is itself and one. So in this case of relatively prime integers, we are trying to get their greatest common factor to be one...even though they might be composite numbers. So I guess from what I understand, "relatively prime" essentially means that the linear combination is prime. I love how the text states, "This is extremely useful." That is a biased statement, and I'd like to see us tell the English majors how "useful" that statement is.
Next thought...I at first was pretty fascinated by the idea that every integer exceeding 1 has a prime factor. Well. That was interesting until I remembered that 1 is a prime number...and everything as 1 as a factor. So, does this corollary even tell us anything? These are the things I wonder about.
And these divisibility rules are pretty fantastic. Why did no one ever tell me that if I summed the digits in a number and it was divisible by three that the number itself was divisible by three? I feel like this information would have caused me much less stress in math over the years. It also would have saved paper because I wouldn't have done so much long division.
The proofs in this unit are really hard to figure out how to do. I wish I could get along with prime numbers. Can we go back to doing even and odd proofs? I liked those. That is all.
No comments:
Post a Comment