MathDB

kP (k + 1) - (k + 1)P (k) = k^2 + k + 1 for all k \in {1, 2, 3, . . . , 21, 22|

Source: Flanders Math Olympiad 2022 p4

December 24, 2022

algebrapolynomial

Problem Statement

Determine all real polynomials

P

of degree at most

22

for which

kP (k + 1) - (k + 1)P (k) = k^2 + k + 1

for all

k \in \{1, 2, 3, . . . , 21, 22\}