Problem #PRU-78578

Problemas Teoría de Números Divisibilidad División con restos. Aritmética de restos Aritmética de restos Métodos Principio de casillas Principio de casillas (otro) Prueba por contradicción

Problem

All integers from 1 to \(2n\) are written in a row. Then, to each number, the number of its place in the row is added, that is, to the first number 1 is added, to the second – 2, and so on.

Prove that among the sums obtained there are at least two that give the same remainder when divided by \(2n\).