MathDB

6

Part of 2022 Polish MO Finals

Problems(1)

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

Source: Poland 73-3-6

3/31/2022
A prime number pp and a positive integer nn are given. Prove that one can colour every one of the numbers 1,2,…,p−11,2,\ldots,p-1 using one of the 2n2n colours so that for any i=2,3,…,ni=2,3,\ldots,n the sum of any ii numbers of the same colour is not divisible by pp.
number theory