MHB POTW Director
- Feb 14, 2012
Determine all pairs of integers $(a, b)$ satisfying the equation $b(a+b)=a^3-7a^2+11a-3$.
I can reduce the problem to finding solutions to the cubic diophantine equation $y^2 = x^3 - 67x - 66$. There are (at least) three solutions $x = -5, -1, 15$, but that's as far as I can go.I believe anemone used some ineq here too, but that thing there seems suspiciously like an elliptic curve.
Hello.This is not a solution.
The pairs $(a,b) = (1,-2),\ (1,1),\ (2,-1),\ (6,-9),\ (6,3)$ are solutions. I believe that these five are the only solutions but I do not see how to prove that.