Chapter 4: Q41E (page 273)
Use the extended Euclidean algorithm to express gcd(26,91) as a linear combination of 26 and 91.
gcd(26,91) = 31
Linear combinations
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Show that is an irrational number. Recall that an irrational number is a real number that cannot be written as the ratio of two integers.
Using the method followed in Example 17, express the greatest common divisor of each of these pairs of integers as a linear combination of these integers.
a) 9,11 b) 33,44 c) 35,78 d) 21,55 e) 101,203 f)124,323 g) 2002,2339 h) 3457,4669 i) 10001,13422
Prove or Disprove that there are three consecutive odd positive integers that are primes, that is odd primes of the form , and .
Describe a procedure for converting decimal (base 10) expansions of integers into hexadecimal expansions.
Answer Exercise 38 for two's complement expansion.
How is the one's complement representation of the difference of two integers obtained from the one's complement representations of these integers?
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