Q .The difference between the square of two consicutive odd integers is always divisible by ?

Let 2x + 1 is our first consicutive odd integer and (2x + 3) is our second consicutive odd integer.

Now calculate the difference between square of both numbers -

( 2x+3 )² - ( 2x + 1 )²

= 4x² + 12x + 9 - ( 4x² + 4x + 1)

= 4x² + 12x + 9 - 4x² - 4x - 1

= 8x - 8

= 8(x-1)

So the difference between the square of two consicutive odd integer is always divisible by 8