Problem 324

Erdős Problem #324: declared status 'open'. Formalized: yes. Does there exist a polynomial $f(x)\in\mathbb{Z}[x]$ such that all the sums $f(a)+f(b)$ with $a<b$ nonnegative integers are distinct? Current best: The Lander, Parkin, and Selfridge conjecture would imply that $f(x)=x^n$ has this property for all $n\geq 5$. Prize: no. Tags: number theory, powers.