Chapter 4: Q47SE (page 307)
The encrypted version of a message is LJMKG MGMXF QEXMW. If it was encrypted using the affine cipher what was the original message?
the original message
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Use exercise 36 to show that if a and b are positive integers, then
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
Show that the binary expansion of a positive integer can be obtained from its hexadecimal expansion by translating each hexadecimal digit into a block of four binary digits.
Find and and verify that . [Hint: First, find the prime factorizations of 92928 and 123552.]
(a) How can an inverse of modulo be used to solve the congruence when ?
(b) Solve the linear congruence .
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