The difference of the squares of two consecutive odd integers is divisible by which of the following integer?8673

To solve the question regarding the difference of the squares of two consecutive odd integers and to determine its divisibility, we can break down the problem as follows:

1. Break Down the Problem

Let the two consecutive odd integers be represented as:

• First integer: $n$
• Second odd integer: $n + 2$

2. Relevant Concepts

The difference of the squares of these two integers can be expressed as: $(n + 2)^2 - n^2$

3. Analysis and Detail

Calculating the difference: $(n + 2)^2 - n^2 = (n^2 + 4n + 4) - n^2 = 4n + 4$ Factoring out the common term: $4n + 4 = 4(n + 1)$

4. Verify and Summarize

The expression $4(n + 1)$ shows that the difference of the squares of two consecutive odd integers is always divisible by $4$.

Final Answer

The difference of the squares of two consecutive odd integers is divisible by $4$.