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+0  
 
 #1
avatar+638 
+2

We can start by replacing b with (a-1).

 

\begin{align*} (a-1)^2\cdot a^0&=7\cdot a^1+1\cdot a^0
\\\Rightarrow\qquad a^2-2a+1&=7a+1
\\\Rightarrow\qquad a^2-9a&=0
\\\Rightarrow\qquad a(a-9)&=0
\end{align*}

 

So we can have 0 or 9.

 

But there is no base 0, so must be base 9. 

 Mar 21, 2018
 #2
avatar+211 
0

thanks

 Mar 22, 2018
 #3
avatar+638 
0

Oh yay! My LaTeX finally worked for once. 

 Mar 30, 2018

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