Question

In: Advanced Math

Prove that there exist infinitely many positive real numbers r such that the equation 2x +...

  1. Prove that there exist infinitely many positive real numbers r such that the equation 2x + 3y + 5z = r has no solution (x,y,z) ∈ Q × Q × Q.

(Hint: Is the set S = {2x + 3y + 5z : (x,y,z) ∈ Q × Q × Q} countable?)

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