WEEK 6
M: Midterm.  
W: Descending sequences of natural numbers. The division algorithm.  
      3.12. Corollary.  There is no infinite descending sequence of natural numbers.  
      4.1. Theorem. Let b > 1 be an integer. Then for every integer x there are unique integers q,r such that
                                 0 \le r <b and x = q · b + r
      PROBLEMS FOR DISCUSSIONS: Book, p.90 Exercise 41, 42, 48, 49, 53, 56, 63, 64
F: Completion of the proof of Thm 4.1. Generalization to polynomials. Euclid's algorithm.
     4.2. Remark. Division algorithm for polynomials.
     4.3. Terminology + Remark. Linear combinations of integers. If d divides integers x1, ..., xn then d divides
                                                   all their linear combinations.
     4.4. Euclid's Algorithm.  
     PROBLEMS FOR DISCUSSIONS:  Book, p.96 Exercise 82, 83, 84 and p.97 Exercise 92, 93.