N3

Part of 2019-IMOC

Problems(1)

2019 numbers adding up to n

Source: 2019 IMOC N3

Prove that there exists

N\in\mathbb{N}

so that for all integer

n > N

2019

pairwise co-prime positive integers with

n=a_1+a_2+\cdots+a_{2019}

2019<a_1<a_2<\cdots<a_{2019}