Im stuck on this homework problem that im not sure if i am doing right and it is due tommorow:

Prove that there is no perfect square of the form 4k+3?

Case 0:

k is even

k=2n for some n in Z

4(2n)+3=8n+3 which is odd so there is no perfect square if k is even

Case 1:

k is odd

k=2n+1 for some n in Z

4(2n+1)+3 = 8n+7 which is not of the form 4k+3 there for there is no perfect square