MathDB

Polynomial involving sum of digits

Source: Turkey Olympic Revenge 2023 P3

March 6, 2023

number theoryolympic revengePolynomialssum of digits

Problem Statement

Find all polynomials

P

with integer coefficients such that

s(x)=s(y) \implies s(|P(x)|)=s(|P(y)|).

for all

x,y\in \mathbb{N}

. Note:

s(x)

denotes the sum of digits of

x

.
Proposed by Şevket Onur YILMAZ