Prove that the sum of the squares of two consecutive odd integers leaves remainder 2 on division by 8

Two consecutive odd integers can be represented by 2x-1 and 2x+1 where x is any integer.

The sum of the squares is 4x²-4x+1+4x²+4x+1=8x²+2. If we divide by 8 we get x² and a remainder of 2.