If $p$ and $q$ both interpolate the data and have degree at most $n$, the <polynomial> $r=p-q$ has the $n+1$ distinct <roots> $x_0,\ldots,x_n$. A nonzero <polynomial> of degree at most $n$ has at most $n$ roots: repeated use of the <factor theorem> would otherwise make a product of $n+1$ linear factors divide it. Hence $r=0$, proving \b[the interpolating <polynomial> is unique].

Solution

Past exam of the options I course of the University of Oxford / 2013 / P / 1 / b / Solution

 Solution (source code)