Determine the total number of ordered pairs(x,y) of positive integers with 2≤ x,y ≤ 2023 that satisfy this equation:

 xlogy(x-4) = ylogx(yx-3) 

(In reply to computer solution by Charlie)

Plugging non-integral values into the formulae results in non-equal values for the LHS and RHS. That explains why the fimplicit plot did not show the y=x^2 curve. Only isolated (integral) values on the curve solve the equation.

Posted by Charlie on 2023-07-30 10:08:52