$(2)(4)_b$ represents a number written in base $b$. For example $21_3 = 7$. How to find the smallest $b$ such that $(17)(3)_b$ is a multiple of $7$?
Assuming,$(17)$ as the single digit,I computed the smallest base to be $32$.Unfortunately,there is no way I could confirm this answer,so I am asking it here.Am i right?