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

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

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

Expert Solution

Colby Messinger answered 1 year ago

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

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Related Solutions

prove that there exist infinitely many primitive Pythagorean triples

(Discrete Math) Prove that the equation 2x² + y² = 14 has no positive integer solutions.

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