Answer:
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
[tex]9^{2}[/tex] - [tex]3^{2}[/tex] = 81 - 9
= 72
ii. 3 and 1,
[tex]3^{2}[/tex] - [tex]1^{2}[/tex] = 9 - 1
= 8
iii. 7 and 5
[tex]7^{2}[/tex] - [tex]5^{2}[/tex] = 49 - 25
= 24
iv. 21 and 13
[tex]21^{2}[/tex] - [tex]13^{2}[/tex] = 441 - 169
= 272
Therefore, it can be observed that the greatest integer that always divides the difference is 8.
