In: Advanced Math
discrete mathematics
1.
Show that if a | b and b | a, where a and b are integers, then a = b or a = -b.
//Ex. 5, Page 208.
2.
Show that if a, b, c, and d are integers such that a | c and b | d, then ab | cd.
//Ex. 6, Page 208.
3.
What are the quotient and remainder when
a) 44 is divided by 8?
b) 777 is divided by 21?
f) 0 is divided by 17?
g) 1,234,567 is divided by 1001?
//(a), (b), (f), and (g) Ex. 10, Page 209.
4.
Determine whether each of these integers is a prime.
a) 19
b) 27
e) 107
f) 113
//(a), (b), (e), and (f) Ex. 2, Page 217.
5.
Find the prime factorization of each of these integers.
a) 39
c) 101
d) 143
f) 899
//(a), (c), (d), and (f) Ex. 4, Page 217.
6.
What are the greatest common divisors of these pairs of integers?
a) 23 * 33 * 55 and 25 * 33 * 52
d) 22 * 7 and 53 * 13
//(a) and (d) Ex. 20, Page 218.
7.
Find gcd(1000, 625) and lcm(1000, 625) and verify that gcd(1000, 625)*lcm(1000, 625) = 1000*625
//Ex. 24, Page 218.