WEEK 7
M: Holiday.  
W: Euclid's algorithm -- completion. Theorem on greatest common divisors.
      4.5. Theorem. If a,b are integers then the gcd(a,b) exists and is unique.
      4.6. Remark. Everything goes through for polynomials.
      PROBLEMS FOR DISCUSSIONS: Book, p.101 Exercise 102 and p.102 Exercise 106, 107, 108, 109  
F: Fundamental theorem of Arithmetic.
    4.7. Proposition. If a | b·c and  a,b are relative primes then  a | c
    4.8. Proposition. If p is a prime and a1, ..., an are integers and  p |  a1 · a2 ·  ··· · an then  p divides at least one
                                of the numbers a1, ... an
    4.9. Corollary. If p, p1, ..., pn are primes and  p |  p1 · p2 ·  ··· · pn  then  p = pk  for some  k.  
    4.10. Theorem. Fundamental Theorem of Arithmetic. 
    PROBLEMS FOR DISCUSSIONS: No new problems. Finish the problems from the previous assignments.