The difference of squares of two consecutive odd integers is divisible by which of the following integers?
Solution
Correct Answer: Option D
Let,
The two consecutive odd integers be (2n + 1) and (2n + 3)
Now
(2n + 3)2 - (2n - 1)2 = (2n + 3 + 2n + 1)(2n + 3 - 2n - 1)
= (4n + 4) × 2
= 4(n + 1) × 2
= 8(n + 1), which is divisible by 8
The two consecutive odd integers be (2n + 1) and (2n + 3)
Now
(2n + 3)2 - (2n - 1)2 = (2n + 3 + 2n + 1)(2n + 3 - 2n - 1)
= (4n + 4) × 2
= 4(n + 1) × 2
= 8(n + 1), which is divisible by 8
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