MathDB
Polynomial being product of the first few consecutive primes at a point $x>n$

Source: Serbia TST 2022 P5

April 20, 2023
number theory

Problem Statement

Given is a positive integer nn divisible by 33 and such that 2n−12n-1 is a prime. Does there exist a positive integer x>nx>n such that nxn+1+(2n+1)xn−3(n−1)xn−1−x−3nx^{n+1}+(2n+1)x^n-3(n-1)x^{n-1}-x-3 is a product of the first few odd primes?
Back to ProblemsView on AoPS