The difference of the squares of two consecutive odd integers is divisible by which of the following integer?8673
Question
The difference of the squares of two consecutive odd integers is divisible by which of the following integer?8673
Solution
Let's denote the two consecutive odd integers as n and n+2 (since odd numbers are 2 units apart).
The difference of their squares is:
(n+2)^2 - n^2
This simplifies to:
n^2 + 4n + 4 - n^2
The n^2 terms cancel out, leaving:
4n + 4
This can be factored to:
4(n + 1)
So, the difference of the squares of two consecutive odd integers is divisible by 4.
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