Chapter 4: Q51E (page 286)
Express each nonnegative integer a less than 15 as a pair (a mod 3, a mod 5).
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38. How is the oneโs complement representation of the difference of two integers obtained from the oneโs complement representations of these integers?
Find the sum and product of each of these pairs of numbers. Express your answers as a base 3 expansion.
a)
b)
c)
d)
Find the prime factorization of 10!.
The value of the Euler -function at the positive integer is defined to be the number of positive integers less than or equal to that are relatively prime to. [Note: is the Greek letter phi.]
Find these values of the Euler -function.
a)role="math" localid="1668504243797" b)role="math" localid="1668504251452" c)role="math" localid="1668504258881"
The odometer on a car goes to up miles. The present owner of a car bought it when the odometer read miles. He now wants to sell it; when you examine the car for possible purchase, you notice that the odometer reads miles. What can you conclude about how many miles he drove the car, assuming that the odometer always worked correctly?
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