What is the greatest integer that always divides the difference of the squares of any two different positive odd integers?

The greatest integer is 8.

Step-by-step explanation:

Odd positive integers are positively directed numbers that can not be divided into to equal values without a remainder. Examples are: 1, 3, 5, 7, 9 etc.

Given the following positive odd integers:

i. 9 and 3

- = 81 - 9

         = 72

ii. 3 and 1,

- = 9 - 1

         = 8

iii. 7 and 5

- = 49 - 25

         = 24

iv. 21 and 13

- = 441 - 169

             = 272

Therefore, it can be observed that the greatest integer that always divides the difference is 8.

it has to be a.

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above