MathDB

Certain integers give all residues modulo k

Source: Kvant Magazine No. 9 2023 M2763

January 9, 2024

number theorysum of digitsmodular arithmetic

Problem Statement

Let

k\geqslant 2

be a natural number. Prove that the natural numbers with an even sum of digits give all the possible residues when divided by

k{}

.
Proposed by P. Kozlov and I. Bogdanov