Chapter 4: Q44E (page 273)
Use the extended Euclidean algorithm to express as a linear combination of 1001 and 100001.
Linear combinations
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a) Define the greatest common divisor of two integers.
b) Describe at least three different ways to find the greatest common divisor of two integers. When does each method work best?
c) Find the greatest common divisor of .
d) Find the greatest common divisor of .
a) What does it mean for a to be an inverse of a modulo m?
b) How can you find an inverse of a modulo m when m is a positive integer and m?
c) Find an inverse of 7 modulo 19.
Find the prime factorization of each of these integers.
a.)39 b) 81 c) 101 d) 143 e) 289 f) 899
Convert the binary expansion of each of these integers to
an octal expansion.
a) (1111 0111)2
b) (1010 1010 1010)2
c) (111 0111 0111 0111)2
d) (101 0101 0101 0101)2
Determine whether the integers in each of these sets are Pairwise relatively prime.
a) 11, 15, 19 b) 14, 15, 21
c) 12, 17, 31, 37 d) 7, 8, 9, 11
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