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