DISCRETE MATH - Number Theory

1. (2) Is 17 odd? _______ Show why or why not using the definition of odd.

2. (2) Is 0.362 a rational number?___________ Show why or why not using the definition of a rational number.

3. (2) Does 4 28? _______Show why or why not.

4. (2) Write 1,200 in standard factored form.

5. (3) If n = 4k + 3, does 8 divide n² - 1?__________Show why or why not.

6. (2) Find 37 div 8 = ____________Find 37 mod 8 = ______________

7. (2) If today is October 23rd, 2017, and it is a Monday, what day of the week is October 23rd, 2020? Explain your reasoning.

8. (2) Two athletes run a circular track at a steady pace so that the first completes one round in eight minutes and the second in ten minutes.If they both start from the same spot at 4:00 P. M., when will be the first time they return to the start together?

9. (2) Simplifyn!_

(n-2)!

10. (2) Find an explicit formula for this sequence:1, -2, 3, -4, 5, -6

11.(2) Write the first four terms of the sequence:

a_j = 1 + 2^j, for all integers j 0.

₃

12.(2) ComputeS1

^{m = 1}3^m