Assume that $(4k + 3) ^ 2 - (4k + 3)$ is not divisible by 4. If this is true, prove that $(4(k+1) + 3) ^ 2 - (4(k+1) + 3)$ is not divisible by 4.
I need to prove this for my induction problem, and I've tried manipulating the second expression as much as I can but haven't arrived at a situation where I can use the first expression. Any help is appreciated, could anyone show me how to do this? Thank you.