Algebraic Proof

Prove algebraically that the sum of the squares of any two odd numbers leaves a remainder of 2 when divided by 4.

Ok so lets say the odd numbers are, 2n+1 and 2n+3

then
(2n+1)² + (2n+3)²
= 8n² + 16n + 10
divide this by 2 because you can...
4n²+8n+5

Prove algebraically that the sum of the squares of any two odd numbers leaves a remainder of 2 when divided by 4.

Ok so lets say the odd numbers are, 2n+1 and 2n+3

then
(2n+1)² + (2n+3)²
= 8n² + 16n + 10
divide this by 2 because you can...
4n²+8n+5

now what? thanks to whoever replies

let the odd numbers be 2n+1 and 2n+1
then...

(2n+1)² + (2n+1)²
= 2(4n² + 4n + 1)
= 8n² + 8n + 2

- remainder 2 at the end.

You have to account for it being ANY two odd numbers. So, A = (2a+1) and B = (2b+1)

So, A^2 + B^2 = 4a^2 +4a^ +1 + 4b^2 + 4b + 1

= 4(a^2 + a + b^2 + b) + 2

ok but you havent divided by 4

...