Let $x^2-ax+b=0$ be a second degree equation, where $x, a$ and $b$ are all positive integers greater than 0. Then, for a given $a$,
- Can we calculate how many different values of $b$ are there?
- Can we calculate the divisors of $b$? And its primality?
- Is there any other "important" characteristic about $b$ that we could obtain?
- (Would it be possible to know the exact values of $b$?)