100 of 100: One Hundred and One
Number Theory
Level
1
The first few powers of 101 all begin with 1, as highlighted by red colors below:
\[ \begin{eqnarray} 101^1 &=& {\color{red}{1}}01 \\ 101^2 &=& {\color{red}{1}}0201 \\ 101^3 &=& {\color{red}{1}}030301 \\ 101^4 &=& {\color{red}{1}}04060401 \\ &\vdots& \end{eqnarray} \]
Is this always the case for all positive integer powers of 101?
Bonus: If it is the case, why? If not, what is the smallest power of 101 that doesn't start with a 1?
by
Jason Dyer