Due 1/14:
7.1: #3, 5a, 11, 12,
7.2: #1bd, 6, 10, 11a,
7.3: #1, 2, 3.
Due 1/21:
Calculate lambda(30) and find all the elements with this order
modulo 30.
Calculate lambda(4000) and find an element with this order modulo 4000.
7.2: #9, 16.
Due 1/28:
9.1: #1ad, 2bc, 5, 6, 8.
17.1: #1.
9.2: #1, 6ac.
9.3: #1ab.
Due 2/4:
No homework, midterm review.
Due 2/11:
14.4: #2, 4.
17.2. # 2, 4, 5ac, 7.
17.3: #1ac, 4.
Question 4 is interesting but be advised of some misprints.
The definition of the Jacobi symbol (a/-1) is wrong, and
(b) and (c) are about the Jacobi symbol and not the Kronecker symbol -
you need to assume that b and b' are odd,
otherwise the results stated are certainly false.
Due 2/18:
11.1: #1a, 5. 11.2: # 1a, 3, 4, 7, 11, 18, 19.
Due 2/25:
11.2: #5ab. 11.3: #1, 4. 11.4: #2, 3.
Due 3/4:
11.2: #13, 19. 11.3: #11. 11.4: #4, 6. 9.
11.5. #1.
Hints: for 19(c), use matrix methods to show that
if p/q=[a0, a1, ... , an, .... , a1, a0] has an odd number of terms
then p is not prime. In fact if p_k/q_k is the kth convergent
then p=p_(2n) is divisible by p_(n-1).
For 19(a), use the fact that in the continued fraction expansion
of any rational number, the last partial quotient a_k is greater than 1.
(There is another expansion where we take the last term equal to
1, but we will not use this form.)
Due 3/11:
11.5: #2, 13.1: #2, 4 (hint: read 13.1.3), 9, 10, 14.5: #6 (hint: read the
paragraph below definition 14.3.1 to see how to go), 8, 9, 11,
14.3: #4.