vieta jumping - Find all possible value of c

Let a and b be non-negative integers. If $\frac{a^2+ab+b^2}{ab-2} = c$ for some non-negative integer c, find all possible values of c.Can somebody give me some hint or tips on how to solve this? I have tried to use a computer to brute-force and found that c must be 0, 6, 13. Any help would be greatly appreciated.EDIT: Proof is needed that there is no other value of c other than 0, 6, 13...Read more

Why do we need the minimum solution of (A, B) with respect to some funtion in Vieta jumping?

I guess the title is self-explanatory, but according to Wikipedia, the second step is to take the minimal solution (A, B): The minimal solution (A, B) with respect to some function of A and B, usually A + B, is taken. The equation is then rearranged into a quadratic with coefficients in terms of B, one of whose roots is A, and Vieta's formulas are used to determine the other root to the quadratic.However, I do not fully see the need to take the minimal solution, can someone explain that step for me?...Read more