For any integer $n$, the expression $n^2 - 1$ is always divisible by 8…

Question

For any integer $n$, the expression $n^2 - 1$ is always divisible by 8 when $n$ is

Accepted Answer

D. an odd integer

If $n$ is odd, write $n = 2k+1$.
Then $n^2 - 1 = 4k(k+1)$.
Since $k(k+1)$ is a product of two consecutive integers it is even
so $4k(k+1)$ is divisible by 8. For even $n$, $n^2-1$ is odd, so not divisible by 8.

Answer

any integer

Answer

an even integer

Answer

a prime number

For any integer $n$, the expression $n^2 - 1$ is always divisible by 8 when $n$ is

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