Chapter 4: Q7RE (page 307)
State the fundamental theorem of arithmetic.
Every positive integer can be decomposed into prime factors in a unique way.
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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 ifis composite if and are integers greater than 1 and is odd. [ Hint: Show that is a factor of the polynomial if is odd.]
36. If m is a positive integer less than , how is the one’s complement representation of −m obtained from the one’s complement of m, when bit strings of length n are used?
Show that if ac = bc (mod m), where a,b,cand mare integers with m > 2and d = gcd (m,c) , then a = bmodm/d .
37. How is the one’s complement representation of the sum of two integers obtained from the one’s complement representations of these integers?
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