difference of two squares (iv)

choose a square number
choose another
subtract one from the other

divide this difference by 4; what can the remainders be?



why can't numbers of the form  4k - 2 (or 4k + 2) be written as the difference of two squares?

how can you obtain numbers that are of the form  4k + 1 (or 4k - 1) by subtracting two squares?