eggplant_burger wrote:
that's a piddling argument. it can be proven that it is a valid proof.
since there are 2 variables to a degree greater than 1 on the left side, and only 1 variable to a degree greater than 1 on the right side, the left will increase more quickly than the right. So if they are already not equal at a point where the values of the left and right side fall into a pattern, they will never be equal. I think that the maximum possible natural number in Turing (4294967294) is reasonably high enough to assume that a pattern will be established. It's like using limits... you don't quite show it exactly, but it's so close it doesn't make a difference.
you may pull it off if its only one variable (after you show exactly when RHS>LHS for all x>x0, and test all solution less than or equal to x0), but with these multiple variables, no.