Chapter 4: Q2E (page 284)
Show that937is an inverse of 13modulo 2436 .
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Convert (1 1000 0110 0011)2from its binary expansion
to its hexadecimal expansion.
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?
Show that a positive integer is divisible by 3 if and only if the sum of its decimal digits is divisible by 3.
What are the greatest common divisors of these pairs of integers?
a)
b)
c) 17,
d)
e) 0, 5
f)
Show that the sum of squares of two odd integers cannot be the square of an integer.
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