MathDB

Sums of numbers of the same colour not divisible by a given prime

Source: Poland 73-3-6

March 31, 2022

number theory

Problem Statement

A prime number

p

and a positive integer

n

are given. Prove that one can colour every one of the numbers

1,2,\ldots,p-1

using one of the

2n

colours so that for any

i=2,3,\ldots,n

the sum of any

i

numbers of the same colour is not divisible by

p