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The difference between the squares of two consecutive odd integers is always divisible by ?

Correct Answer: 8

Explanation:

Let the two consecutive odd integers be (2x + 1) and (2x + 3)
Then,


(2x + 3)2 - (2x + 1)2


= (2x + 3 + 2x + 1) (2x + 3 - 2x - 1)


= (4x + 4)(2)
= 8 (x + 1), which is always divisible by 8


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