If 4 divides a^2-3b^2, then at least one of the integers a and b is even.

Step-by-step explanation:

The proof can be done by contradiction. Suppose both a, and b weren't even. So that a, and b are both odd. This means they both look like

(for some integers k and l)

So, let's compute what would be in this case:

which notice wouldn't be divisible by 4. This shows then that since is divisible by 4, at least one of the integers a and b is even.

1. d.90

2. e. none of these (80)

3. a. 0

4. b. 6

5. e. none of these (10)

6. a. 5

47 - 90 = 43

43 - 180 = x

x = 137