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Verify it for $n\le 5$, suppose $n\ge 6$. Note that $6^n+1\equiv 1\pmod{2}$ and $\equiv 2\pmod{5}$, yielding its last digit to be $7$. Hence, $6^n+1=\overline{77\cdots 7}$.
NT Game
Determine the sum of all positive integers $n$ such that the decimal representation of the number $6^n + 1$ has all its digits the same.
Number Theory
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