PROVE THE FOLLOWING STATEMENTS :

If a number is of the type 4k + 2 it is even.

If an even number is square, then it is the square of an even number, not the square of an odd number.

Square of an even number, say 2n, is 4n^2, which is a multiple of 4. So if an even number is a square, it has to be a multiple of 4.

But 4k+2 is not a multiple of 4. When you divide it by 4 you get a remainder of 2, not zero.