Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have a system of equations of the form $a_i\alpha+b_i\beta+c_i\gamma+d_i\delta=2$. All coefficients are positive integers, and I also have the extra restriction that $0<\alpha,\beta,\gamma,\delta<1$.

My question is whether there exists a technique to easily determine whether this system implies that $\alpha=\beta$? (or any other combination of variables, but I do need to be able to ask the question for a specific pair of variables) I'm especially looking for techniques that can easily and efficiently be implemented in a computer program.

Maybe it is also best that I mention that I'm looking for cases where there is a solution if and only if those two variables are equal, and not the cases where there is a solution such that they might be equal. An example is if there is an equation with coefficients $(x,y,z,u)$ and one with coefficients $(y,x,z,u)$, such that not both $x$ and $y$ are equal to zero. These are some cases, but there are still other situations that also imply the equality, but that I'm missing if I only perform that check.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.