M2763

Part of Kvant 2023

Problems(1)

Certain integers give all residues modulo k

Source: Kvant Magazine No. 9 2023 M2763

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

number theorysum of digitsmodular arithmetic