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 n = ap(-b)P + ap-1(-b)P-1 + and 0 < a; < b. Write a) 714-g in decimal b) 1035-7 in decimal c) 97 in base -2 + az(-b)² + a¡(-b) + ao ...

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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 = ap(-b)P + ap-1(-b)P-1 +
and 0 < a; < b. Write a) 714_g in decimal b) 1035_7 in decimal c) 97 in base -2
+ az(-b)² + a1(-b) + ao
...
-8-
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, ... , ap such that n = ap(-b)P + ap-1(-b)P-1 + and 0 < a; < b. Write a) 714_g in decimal b) 1035_7 in decimal c) 97 in base -2 + az(-b)² + a1(-b) + ao ... -8-
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