9/29/04 (due 10/13/04)
The following problems are all taken from the handout on Number Theory
from Rosen's book.
(Note: I took off three problems that were up there earlier today,
because I inadvertantly assigned them last week -- I had meant to assign
them for this week and added 1 -- number 28. The good news is that you -->
-- have less to do this time
around.)
Section Number Points Comments
2.6 2(b),(f) 6 For (f), use the Euclidean algorithm to
compute the gcd and then back substitute
8 3
10 4
12 3
15 4
18 3
20 5 Note that you can't immediately apply the CRT,
since 6, 10, and 15 are not pairwise relatively prime.
You need to convert it to a form where you can apply
the CRT. (Hint: if x is congruent to 5 mod 6,
what is x congruent to mod 2 and mod 3?)
26 3
28 5 (Hint: for part (b), set up a system of
congruences mod 5, 7, and 11 of which
3**302 is a solution; then find another solution.
48 4 There seems to be a bug in Rosen's description of the
Euclidean algorithm. Rosen says (just before Exercise 48)
that tj = t(j-1) -q(j-1)t(j-2). It should say
tj=t(j-1) - qj t(j-2). I'll accept any reasonable
backsubstitution approach to computing the coefficients.