Proof: (Pigeon Hole Principle) from a Problem Solving Class

[rad0786]

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

Homework Equations

|a + sqrt(2)*b + cuberoot(3)*c| < 10^-11

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?

 

[rad0786]

Never mind people, after a lot of hard thinking, i got it (well...close to it!)