IMO 2022 Problem 3

Proposed by: -
Verified: no
Verdicts: UNKNOWN + UNKNOWN
Solve time: 42s

Problem

Let $k$ be a positive integer and let $S$ be a finite set of odd prime numbers. Prove that there is at most one way (up to rotation and reflection) to place the elements of $S$ around a circle such that the product of any two neighbours is of the form $x^2 + x + k$ for some positive integer $x$.

Working