Chapter 4: Q17SE (page 307)
Use Dirichlet’s theorem, which states there are infinitely many primes in every arithmetic progression ak + b where gcd(a, b) =1, to show that there are infinitely many primes that have a decimal expansion ending with a 1.
Take a = 10 and b = 1 .
Over 22 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Using the method followed in Example 17, express the greatest common divisor of each of these pairs of integers as a linear combination of these integers.
a) 10,11 b) 21,44 c) 36,48 d) 34,55 e) 117,213 f)0,223 g) 123,2347 h) 3454,4666 i) 9999,11111
38. How is the one’s complement representation of the difference of two integers obtained from the one’s complement representations of these integers?
32. Show that a positive integer is divisible by 11 if and only if the difference of the sum of its decimal digits in even- numbered positions and the sum of its decimal digits in odd-numbered positions is divisible by 11.
Describe an algorithm to add two integers from their Cantor expansions.
Use the extended Euclidean algorithm to express as a linear combination of 245 and 356
What do you think about this solution?
We value your feedback to improve our textbook solutions.
