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The difference between the square of two consecutive odd integers is always divisible by :
Answer & Solution
Correct Answer:
Option
D
Let the two consecutive odd integers be (2m + 1) and (2m + 3)
Then, (2m + 3)2 - (2m + 1)2
= [(2m + 3) + (2m + 1)] [(2m + 3) - (2m + 1)]
= (4m + 4) × 2
= 8m + 8
= 8(m + 1), which is always divisible by 8
Then, (2m + 3)2 - (2m + 1)2
= [(2m + 3) + (2m + 1)] [(2m + 3) - (2m + 1)]
= (4m + 4) × 2
= 8m + 8
= 8(m + 1), which is always divisible by 8
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