Powers of 101

Algebra Level 3

The first few powers of 101 all begin with 1, as highlighted by red colors below: 1011=1011012=102011013=10303011014=104060401. \begin{aligned} 101^1 &=& {\color{red}{1}}01 \\ 101^2 &=& {\color{red}{1}}0201 \\ 101^3 &=& {\color{red}{1}}030301 \\ 101^4 &=& {\color{red}{1}}04060401 \\ &\vdots.& \end{aligned} Is that always the case for all powers of 101?

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