1. The problem statement, all variables and given/known data Prove that THEIR EXISTS INTEGERS a,b,c NOT ALL 0 AND EACH OF ABSOLUTE VALUE <10^6 SUCH THAT |a + sqrt(2)*b + cuberoot(3)*c| < 10^-11 2. Relevant equations |a + sqrt(2)*b + cuberoot(3)*c| < 10^-11 3. The attempt at a solution Well, I know that we have to use the pigeon hole principle, otherwise I am completely lost. I did try to actually find values for a,b,c ... but no luck with that. I am now attempting to rearrange the formula and solve for some variable in terms of another. Has anybody seen a problem like this before? Does it have a name?