Homework assignments for Math 322

Dr.  Z. Zeng

Homework 1, 05/21
Section 2.1: #2, 3, 5, 7, 8, 15, 16
Section 2.2: #Exercise on page 17, 5, 10
Homework 2, 05/23
Section 2.3: #3, 4, 5, 6, 8, 10
Section 2.4: Factor 227981, 243936
Section 2.5: #3, 5, 7
Homework 3, 05/30
Section 2.5: #1(a,b) Do the following:
               (i)  Find GCD and LCM using prime decompositions:
                      781=(11)(71),   994=(2)(7)(11)
                      5950=(2)(5)(5)(7)(17), 13300=(2)(2)(5)(5)(7)(19)
               (ii) Find GCD using the Euclidean algorithm
               (iii) Find x, y such that ax+by=(a,b)
             #8
Section 2.6: #1(a,b,c), 8, 9
Page 517, #1
Homework 4, 06/04
Section 3.1: #1, 2, 3, 5, 7, 8, 12, 14
Homework 5, 06/06
Section 3.2: #1, 2, 4, 5, 8
Homework 6, 06/11
Section 3.3: #1, 2, 4, 5 (#5 partially. Set up the problem that m_i's
are relatively prime)
Homework 7, 06/13
Section 3.4: #Exercise on page 83
             #1 by Maple
             #2(a) by Chinese Remainder Thm
             #5
Section 4.1: #1, 2, 3, 4
Homework 8, 06/18
Section 3.4: (i) #6, Page 107
            (ii) #7 page 107
           (iii) The first asertion of #10, page 107, namely
                 Let n=r^4+1. Show that 3, 5 and 7 can not divide n
            (iv) #9, extra credit, not required
             (v) #1 page 110
            (vi) Show that if (x,mn)=1, then (x,m)=(x,n)=1.
Homework 9, 06/20
Section 4.3: #1, 3, 5, 8, 10