Recent content by rdr3

  1. R

    Intro to Proofs: Greatest Common Divisors

    So maybe this? Suppose d[SIZE="4"]∤c... Then c≠nd In which case, c≠nd≠(nx0)a+(ny0)b. So like that? Or am I way off? Sorry I'm not very good at this... The teacher explains things way over everyone's head.
  2. R

    Intro to Proofs: Greatest Common Divisors

    Homework Statement (a) Let a and b be integers with gcd(a,b)=d, and assume that ma+nb=d for integers m and n. Show that the solutions in Z to xa+yb=d are exactly x=m+k(b/d), y=n-k(a/d) where k∈Z. (b) Let a and b be integers with gcd(a,b)=d. Show that the equation xa+yb=c...
  3. R

    Introduction to Proofs: One-to-One and Onto Problem

    1. Given: Let f: X → Y be a function. Then we have an associated function f-1: P(Y) → P(X), where f-1 (B)⊂X is the inverse image of B⊂Y. Question: Show that f^(-1) is one-to-one if and only if f is onto. [Notes: ⊂ represents subspace, I just couldn’t find a way to put the line under the...