Originally Posted by

**sixstringartist** Ahoy all late nighters. looking for a some clarity on a problem I have. Please go easy. Im sure to screw something up when writing this.

Ok so heres the problem as I know it. It is an algorithm with the following behavior:

$\displaystyle {t}_{0} = 0 \\ {t}_{1} = {t}_{0}*17 + {x}_{0} \\ {t}_{2} = {t}_{1}*17 + {x}_{1} \\ {t}_{3} = {t}_{2}*17 + {x}_{2} \\ \vdots \\ {t}_{n} = {t}_{n-1}*17 + {x}_{n-1} \\ $

which I believe is the following series

$\displaystyle {t}_{n} = 17^{n-1}{x}_{0} + 17^{n-2}{x}_{1} + \hdots + 17^{1}{x}_{n-2} + 17^{0}{x}_{n-1}$

Now all the $\displaystyle {x}_{n}$'s are unknown and are an integer in the range 1-26

Given a value for $\displaystyle {t}_{n}$ can a unique sum be found? I suspect there will be multiple solutions. Could someone help me simplify this?

If it helps, assume $\displaystyle {t}_{n} = 22640$