We have a positive definite binary form of degree . I have to prove, without using lower bounds on linear forms in logarithms (we were working with Baker's theorems), that for each positive integer m the equation has only finitely many solutions in . I also have to describe a method to find these.
We know that the coefficient of of is positive, and that all zeros of are in . We also know the discriminant of is negative.
I have trouble finding this out by myself. I also looked up some number theory books, but most literature is about binary quadratic forms, not the binary form I have to prove this for. Hope someone can help me!