I have problems proving the uniqueness of simple continued fraction representation of rational numbers as claimed in http://en.wikipedia.org/wiki/Continued_fraction#Finite_continued_fractions.
Let $r$ be a rational number with representation $[p_0,p_1,...,p_n]$ where $p_n\neq 1$. I want to prove that this representation is unique, i.e. if $[q_0,q_1,...,q_m]$ is another representation then $m=n$ and the $p$'s are equal to the $q$'s.
I know that this must be done by induction on $n$ but somehow I dont know how to proceed, even in the base case (that is $p_0\neq 1$ and conclude $m=0$). Any hints is much appreciated.