M201: First graded homework

For each question, state the proposition and write a formal proof.
  1. (3 points.) If  x  is an integer, then  x2 - 3x +6  is even.

  2. (3 points.) If  x  is an integer, and  x2 - 3  is odd, then  x  is even.

  3. (3 points.) There are no integers  x, y 
    such that  20x - 15y = 1.