Problem #PRU-98579

Problems Calculus Real numbers Integer and fractional parts. Archimedean property

Problem

Are there such irrational numbers $a$ and $b$ so that $a > 1$ , $b > 1$ , and $⌊ a^{m} ⌋$ is different from $⌊ b^{n} ⌋$ for any natural numbers $m$ and $n$ ?

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