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Chapter 4: Number Theory and Cryptography

Expert-verified
Discrete Mathematics and its Applications
Pages: 237 - 307
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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Illustration

342 Questions for Chapter 4: Number Theory and Cryptography

  1. Solve the congruence 2x=7mod17using the inverse of 2 modulo 7 found in part (a) of Exercise 6.

    Found on Page 284

  2. Explain why both 3792 and 2916 would be bad choices

    Found on Page 292

  3. What are the quotient and remainder when

    Found on Page 244

  4. Convert each of the integers in Exercise 6 from a binary expansion to a hexadecimal expansion.

    Found on Page 255

  5. Determine whether there is a key for which the enciphering function for the shift cipher is the same as the deciphering function.

    Found on Page 304

  6. Show that if2m+1is an odd prime, then m=2n for some nonnegative integer n. [Hint: First show that the polynomial identity xm+1=xk+1xk(t−1)−xk(t−2)+…−xk+1 holds, wherem=ktandt is odd.]

    Found on Page 272

  7. a) How can you find a linear combination (with integer coefficients) of two integers that equals their greatest common divisor?

    Found on Page 307

  8. Develop a test for divisibility of a positive integer nby 3based on the binary expansion of n.

    Found on Page 307

  9. Convert (1011 0111 1011)2from its binary expansion to

    Found on Page 255

  10. Show thatlog23 is an irrational number. Recall that an irrational number is a real number xthat cannot be written as the ratio of two integers.

    Found on Page 272

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