Find an even number that can be represented as difference of two squares in exactly 3 ways or prove that none exists. Find an even number that can be represented as difference of two squares in exactly 3 ways or prove that none exists.


I tried many different numbers and nothing is working but I don't know how to prove that it isn't possible.
$$64 = 17^2-15^2 = 10^2-6^2 = 8^2 - 0^2$$

Unless you are also counting $(-17)^2 -(-15)^2$, $(-17)^2-15^2$, etc. as different ways. 



Don't like subtracting $0^2$? 

$$256 = 65^2-63^2 = 34^2-30^2 = 20^2-12^2$$
I found $80$ 

$80=9^2-1^2=12^2-8^2=21^2-19^2$