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3. Suppose b > 1 is an integer. The proof of the existence of a base b representation of any integer n can be modified to prove that there are integers ao, a1, ..., ap such that n = a,(-b)P + ap-1(-b)P-1 + .…+ az(-b)² + a;(-b) + ao < b. Write a) 714-g in decimal b) 1035_7 in decimal c) 97 in base -2 d) -883 in and 0 < ai base -10

3. Suppose b > 1 is an integer. The proof of the existence of a base b representation of any integer n can be modified to prove that there are integers ao, a1, ..., ap such that n = a,(-b)P + ap-1(-b)P-1 + .…+ az(-b)² + a;(-b) + ao < b. Write a) 714-g in decimal b) 1035_7 in decimal c) 97 in base -2 d) -883 in and 0 < ai base -10

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 10E: Let be a nonzero integer and a positive integer. Prove or disprove that .
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3. Suppose b > 1 is an integer. The proof of the existence of a base b representation of any integer n can be modified to prove that there are integers ao, a1, ... , a, such that п %3D а, (-b)Р + ар-1(-b)?-1 + .... + a2(-b)² + a1(-b) + ao n = and 0 < a; < b. Write a) 714_g in decimal b) 1035-7 in decimal c) 97 in base –2 d) –883 in base –10
Transcribed Image Text:3. Suppose b > 1 is an integer. The proof of the existence of a base b representation of any integer n can be modified to prove that there are integers ao, a1, ... , a, such that п %3D а, (-b)Р + ар-1(-b)?-1 + .... + a2(-b)² + a1(-b) + ao n = and 0 < a; < b. Write a) 714_g in decimal b) 1035-7 in decimal c) 97 in base –2 d) –883 in base –10
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