The Fundamental Theorem of Arithmetic has a neat result but I found myself lost in the proof. The first question arose on page 257 when it says that "by the induction hypothesis, each of a and b is prime or can be expressed as a product of primes." Is this just a restatement of what we are trying to prove? Because if not that almost seems backwards. Right after this sentence it goes on to say that by the principle of induction, that the theorem is true. Next question deals with Theorem 11.20, dealing with the relation between n^.5 being rational and an integer. While writing this I actually figured it out...I think that the use of several theorems that we have proved in the past was a little confusing.
We talked about this today in class, but the shortcuts for divisibility of several numbers are really neat! We had learned certain parts of these growing up and now it's neat to be able to see why they work. I really enjoyed the rules for 3, 9 and 8. However, 11 seems to me just a little too much work! Although I'm not sure why it works and how useful perfect numbers are, perfect numbers are super cool. Is that just a coincidence for why the numbers are a sum of 1 to the largest prime divisor?
No comments:
Post a Comment