The other tutor just wrote 4, which is wrong, with
no explanation at all. I have no idea why he would
do that.
Here is the explanation and answer:
aČ - bČ = 391
(a - b)(a + b) = 391
The only ways to factor 391 are
391·1
and 23·17
We will first consider a and b to be positive
So we have either the system
which has solution a=196, b=195
or
which has solution a=20, b=3
Since a and b are squared in the original equation, we may
choose either sign, so these are the integral solutions:
1. a = 196, b = 195
2. a = 196, b = -195
3. a = -196, b = 195
4. a = -196, b = -195
5. a = 20, b = 3
6. a = 20, b = -3
7. a = -20, b = 3
8. a = -20, b = -3
So there are 8 solutions.
Edwin