Question 150
A polynomial $P(x)$ is a base-$n$ polynomial if it is of the form $a_{d} x^{d} + a_{d-1} x^{d-1} + \cdots + a_{1} x + a_{0}$, where each $a_{i}$ is an integer between $0$ and $n-1$ inclusive and $a_{d} \gt 0$. Find the largest positive integer $n$ such that for any real number $c$, there exists at most one base-$n$ polynomial $P(x)$ for which $P(\sqrt{2} + \sqrt{3}) = c$.
Proposed by: James Lin
Proposed by: James Lin