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**1. Homework Statement**

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. Homework 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?