Date: Tue, 10 Dec 1996 16:52:02 GMT
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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:
- page 181, Problem 8. Instead of part (b), give an indirect proof of
the following: "If n squared is odd then so is n."
- page 181, Problem 10
- Prove or disprove that n*n + n + 1 is always prime.
- 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.)
- page 182, Problem 24
- page 182, Problem 40
- page 182, Problem 44
- (Bonus) page 182, Problem 32
- (Bonus) page 182, Problem 36
- (Bonus) Prove that any prime number bigger than 3 leaves
remainder of 1 or 5 when divided by 6.