0

I found a class of equations with the following form. $$A (Bm)^k | (Cm^2 + Dm + E)^n$$

$ m \ge 12$ can be any rational number, $n > k$ are natural numbers.

$ 0 < A < 1$ is fixed and the rest of the constants are fixedintegers A*(Bm)^k needs to be an integer.

My intuition says that there should be none but I don't know how to prove it either way.

Edit: Some more explanation of my intuition. I'd think that the right would increase too fast to be smaller than the right.

ruler501
  • 1,218
  • With so many free parameters in there, I'd be surprised if there weren't any examples. – Semiclassical Aug 05 '14 at 00:48
  • If you say for example that $A,B,C,D,E$ are to be fixed rationals and you want the form to represent all rationals, with $m$ restricted to be a rational $m \ge 12$, then the problem makes sense. Or if you say given any rational one can choose some particular $A,B,C,D,E$ and an $m \ge 12$ to represent it, that is another problem. In summary, your question needs more specific information. – coffeemath Aug 05 '14 at 00:49
  • I edited in the other constraints. Thanks for reminding me – ruler501 Aug 05 '14 at 00:50
  • It still remains whether the constants are to be fixed in advance, or else are to be chosen so as to represent each given rational. – coffeemath Aug 05 '14 at 00:51
  • 1
    What equation? I see no $=$. And in the context of rational numbers what does $|$ mean? – Robert Israel Aug 05 '14 at 00:52
  • Added the suggestions to fix the question. – ruler501 Aug 05 '14 at 01:45
  • And I really just want to know how would you go about solving these kinds of forms. I don't necessarily want a solution. – ruler501 Aug 05 '14 at 02:16

0 Answers0