Are there exist some positive integers $n$ and $k$, such that the first decimals of $2^n$ (from left to the right) represent the number $5^k$ while the first decimals of $5^n$ represent the number $2^k$ ? (5)
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Tags: number theory
Are there exist some positive integers $n$ and $k$, such that the first decimals of $2^n$ (from left to the right) represent the number $5^k$ while the first decimals of $5^n$ represent the number $2^k$ ? (5)