Chapter 4: Q27SE (page 307)
Find gcd(2n + 1.3 + 2), where n is a positive integer.[Hint: use the Euclidean algorithm]
To find gcd(2n + 1.3n + 2) is 1
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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
Use the extended Euclidean algorithm to express as a linear combination of 1001 and 100001.
Convert each of the integers in Exercise 6 from a binary expansion to a hexadecimal expansion.
a) (1111 0111)2
b) (1010 1010 1010)2
c) (111 0111 0111 0111)2
d) (1010 1010 1010 101)2
a) Describe a procedure for finding the prime factorization of an integer.
b) Use this procedure to find the primefactorization of 80,707.
Prove or Disprove that there are three consecutive odd positive integers that are primes, that is odd primes of the form , and .
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