Question

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

Answer 1

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

$9^{2}$ - $3^{2}$ = 81 - 9

         = 72

ii. 3 and 1,

$3^{2}$ - $1^{2}$ = 9 - 1

         = 8

iii. 7 and 5

$7^{2}$ - $5^{2}$ = 49 - 25

         = 24

iv. 21 and 13

$21^{2}$ - $13^{2}$ = 441 - 169

             = 272

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