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I'm pretty sure this is right but not 100%. Directions are as follows:

GIve a reason for your answer in each of 1-13. Assume that all variables represent integers.

If n = 4k + 3, does 8 divide n^2-1? Here is my answer:

No. n^2-1 = (4k+3)^2-1 = (4k+3)(4k+3)-1 = (16k^2+24k+9)-1 = 16k^2+24k+8 = 16(k+1/2)(k+1). K+1 is an integer but k+1/2 is not necessarily an integer, because 1/2 is not an integer.

Is my reasoning correct? thanks!