If a number is represented as 1234 in base a and as 1002003004 in base b, what can you say about bases a and b?
I have that for numbers x and y, $x_{a}=1*a^3+2*a^2+3*a+4*b^0$ and that $y_{b}=1*b^9+2*b^6+3*b^3+4*b^0$. I just cannot see a connection other than that the bases from a are 3 times as big? I just don't think this is the answer they are looking for.
Thanks in advance for any help!
$x_a=y_b$ gives $(a-b^3)(a^2+b^6+ab^3+2a+2b^3+3)=0$ , as $a,b>0$ which means the above expression=0 only if $a=b^3$