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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Find the prime factorization of each of these integers.
a.)39 b) 81 c) 101 d) 143 e) 289 f) 899
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.
Answer Exercise 35if each expansion is a two's complement expansion of length five.
35 What integer does each of the following one's complement representations of length five represent?
a)11001
b)01101
c)10001
d)11111
a) Describe a procedure for finding the prime factorization of an integer.
b) Use this procedure to find the primefactorization of 80,707.
Show that a positive integer is divisible by 3 if and only if the sum of its decimal digits is divisible by 3.
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