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Prove that there exist infinitely many positive real numbers r such that the equation 2x + 3y...

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Advance Math

  1. Prove that there exist infinitely many positive real numbersr such that the equation 2x +3y + 5z = r has nosolution (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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