Chapter 4: Q57E (page 286)
Write out a table of discrete logarithms modulo 17 with respect to the primitive root 3.
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a) Define what it means for a and b to be congruent m odulo 7.
b) Which pairs of the integers-11,-8,-7,-1,0,3 and 17are congruent ?
c) Show that ifa and bare congruent m odulo 7, then 10a+13 and -4b+20 are also congruent m odulo 7.
Show that the sum of squares of two odd integers cannot be the square of an integer.
a) Explain why ndiv 7 equals the number of complete weeks in days.
b) Explain why n div 24 equals the number of complete days inn hours.
35. What integer does each of the following one’s complement representations of length five represent?
a) 11001 b) 01101 c) 10001 d) 11111
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
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