So I have concluded that the statement is false however i'm having a hard time explaining them, or writing a proof which I need to do for full marks. Could any one help me in explaining this, please be thorough so that I could understand more of proving these types of questions.
edit: I am no longer sure than the statement is false. I have tried my example again and have realized that I made a mistake. Now I need clarification on whether it is false or not.
2nd edit: Okay my progress is that, in order for the first equation to be true a must be an even number and b must be odd, we then get a modulus of 4 for all even integers a and odd integers b. I have tried many examples and they all turn out to be true. Again i'm having a hard time explaining or proving why.