Chapter 4: Q2E (page 304)
Encrypt the message STOP POLLUTION by translating the letters into numbers, applying the given encryption function, and then translating the numbers back into letters.
a) f(p)=(p+4) mod 26
b) f(p)=(p+21) mod 26
c) f(p)=(17 p+22) mod 26
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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?
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) 10,11 b) 21,44 c) 36,48 d) 34,55 e) 117,213 f)0,223 g) 123,2347 h) 3454,4666 i) 9999,11111
Determine whether the integers in each of these sets are Pairwise relatively prime.
a) 21, 34, 55 b) 14, 17, 85
c) 25, 41, 49, 64 d) 17, 18, 19, 23
Show that the hexadecimal expansion of a positive integer can be obtained from its binary expansion by grouping to-gather blocks of four binary digits, adding initial zeros if necessary, and translating each block of four binary digits into a single hexadecimal digit.
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 .
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