Date: Tue, 10 Dec 1996 16:52:02 GMT Server: NCSA/1.4.2 Content-type: text/html CSE 321 Assignment #3

CSE 321 Assignment #3
Autumn 1996

Due: Friday, October 18, 1996.

Reading Assignment: Read sections 3.1 and 3.2 of the text and skim the supplementary logic notes. The following problems are from the Third Edition of the text.

Practice Problems: page 181, Problem 9; page 182, Problem 15

Problems:

  1. page 181, Problem 8. Instead of part (b), give an indirect proof of the following: "If n squared is odd then so is n."

  2. page 181, Problem 10

  3. Prove or disprove that n*n + n + 1 is always prime.

  4. Prove that the square of an integer not divisible by 6 leaves a remainder of 1, 3 or 4 when divided by 6. (Hint: Use a proof by cases, one case per possible remainder when the integer is divided by 6.)

  5. page 182, Problem 24

  6. page 182, Problem 40

  7. page 182, Problem 44

  8. (Bonus) page 182, Problem 32

  9. (Bonus) page 182, Problem 36

  10. (Bonus) Prove that any prime number bigger than 3 leaves remainder of 1 or 5 when divided by 6.