57 views

Consider polynomials in a single variable $x$ of degree $d$. Suppose $d < n/2$. For such a polynomial $p(x)$, let $C_{p}$ denote the $n$-tuple $(P\left ( i \right ))_{1 \leq i \leq n}$. For any two such distinct polynomials $p, q,$ the number of coordinates where the tuples $C_{p}, C_{q}$ differ is.

1. At most $d$
2. At most $n - d$
3. Between $d$ and $n - d$
4. At least $n - d$
5. None of the above.