Is there $k\in\mathbb{R}-\mathbb{Z}$ such that $2^k\in\mathbb{N}$ and $3^k\in\mathbb{N}?$ My guess is no such $k$ exists but seems hard to prove. Any ideas? Thanks in advance
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Is there $k\in\mathbb{R}-\mathbb{Z}$ such that $2^k\in\mathbb{N}$ and $3^k\in\mathbb{N}?$ My guess is no such $k$ exists but seems hard to prove. Any ideas? Thanks in advance
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