Graders' comments

HW1

  Only 2 people got 1.4.14 right in the entire class. 
  Almost everyone had a problem figuring out what it was
  they were supposed to prove.  Virtually everyone
  assumed that t (the remainder) was given as odd, and
  just proved that |t|<b.  

  Some people are apparently confused about a|b.  A few
  people seemed to think that the phrase "a divides b"
  was exactly the same as the object "a divided by b."  

HW2,3

  On last weeks set, a lot of people had some
  misunderstandings about the gcd.  Most common (as far
  as I remember) were, if (a,b)=d and (a,c)=e, what
  (a,b+c) might be.  I can't remember any specific
  examples, though.

  On this weeks set, only 4 people got 3.6.22.  Most
  people didn't really make any attempt at all. 
  Otherwise, there were no systematic problems.

HW4

  The only systematic problem that I can remember was
  with problem 18, sec. 4.2.  A lot of people were able
  to get that p|(x+y)(x-y) implies x=y mod p or x=-y mod
  p.  For some reason, most of them didn't notice that
  it was an "or", not an "and", and added the two
  equations.  The result was that x=0 mod p, so there
  must be no solutions. 

  Some people also assumed that (x^2 , p) = p or 2 on
  problem 18.  I have no idea why.  

HW5

  Everything was pretty good (it was the highest average
  homework), but not many people turned it in.  The only
  strange mistake I can remember was a few people
  claiming that 

  x=1 modp
  x=1 mod q
  Then x+y = 1(modp) + 1(modq) = 1mod(pq)

  I'm not sure where this idea came from. 

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