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33=2734=8135=24336=72937=218738=6561\begin{array} { r c r } 3^3 &=& {\color{#D61F06}{2}}7 \\ 3^4 &=& {\color{#D61F06}{8}}1 \\ 3^5 &=& 2{\color{#D61F06}{4}}3\\ 3^6 &=& 7{\color{#D61F06}{2}}9\\ 3^7 &=& 21{\color{#D61F06}{8}}7 \\ 3^8 &=& 65{\color{#D61F06}{6}}1 \end{array} 333435363738======278124372921876561
The above shows the first few powers of 3, starting from 333^333. Is it true that the second last digit (from the right) of 3n3^n3n for integers n (>2)n\,(> 2)n(>2) is always an even number?
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