Erdős problem 324 · problems.science

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?

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2 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

324.lean

Retained formal statement2 of 2

Probably $f(x) = x^5$ has the property that the sums $f(a)+f(b)$ with $a < b$ nonnegative integers are distinct.

FormalConjectures/ErdosProblems/324.leanErdos324.erdos_324.variants.quintic5 linesExact file

1Set.InjOn2  (fun x =>3    match x with4    | (a, b) => a ^ 5 + b ^ 5)5  {(a, b) | a < b}

OpenStatement only, no proof