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  1. K

    Various Proofs Regarding Divisors and Properties of Divisors

    How can one have Physics without Mathematics? Love them both. Thank you again for your help and (perhaps more importantly) your time. As I read through Spivak's book, I will likely find myself on this wonderful site once again. I hope we bump into each other (in whatever ways one could "bump"...
  2. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Okay. Sounds good. Thank you very much and thanks for the wonderful recommendations for books. By the way, I like your remake of Oppenheimer's quote (or rather, the Bhagavad Gita). Is it safe to assume that you are either a physicist, a physicist in progress, or a polymath?
  3. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Well, what I have applied to is a double major in Mathematics and Physics. I want to become a theoretical physicist as I have a great passion for the study of nature. However, that said, I also very much enjoy pure mathematics. My knowledge in the area of mathematics extends through elementary...
  4. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Thank you again. Now, I have a few final questions. Forgive me for bothering you but I have no guidance. I notice that in a lot of these books, a lot of knowledge in other fields of mathematics is assumed. I am not yet in university and I have no structure in the subject or an order in which to...
  5. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Okay. Thank you very much! I realize that saying it is not enough. I was just wondering why the site did not move forward in showing that the converse was in fact true. Is it considered acceptable to not state such a thing in a proof that relies on such an argument?
  6. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Hello, I found the following proof on a website for proposition 3. http://www.cut-the-knot.org/Generalization/RationalRootTheorem.shtml When the proof is completed it states "so a and bc are coprime". Now I noticed that what was done was a factorization of the expression in the form...
  7. K

    Various Proofs Regarding Divisors and Properties of Divisors

    I apologize. I did not look at the definition of contrapositive. Again, I found the "proof" online and wanted to move quickly in proving proposition 3. I assumed converse and contrapositive were equal. My mistake. I will post a proof of proposition 3 in a moment obviously without the use of...
  8. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Why do you first say "I'm sure it was extremely simple" and then go on to state "only sad that the proposition isn't true"? That makes no sense. The contrapositive I talk of was found online. Assuming that proposition 1 is true, proposition 2 can be "proven" as follows. Assume α does not...
  9. K

    Various Proofs Regarding Divisors and Properties of Divisors

    Hello there. I have been reading G.H. Hardy's book "A Course of Pure Mathematics". It is a fantastic introduction to Analysis. I have no problems with the book so far, however, it does assume some knowledge in number theory. I just want to make sure that the following proofs for properties of...
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