4

Part of 2019 Baltic Way

Problems(1)

Find all possible values of x_1x_2 + x_2x_3 + ... + x_{k-1}x_k

Source: 2019 Baltic Way P4

Determine all integers

n

for which there exist an integer

k\geq 2

and positive integers x_1,x_2,\hdots,x_k so that x_1x_2+x_2x_3+\hdots+x_{k-1}x_k=n\text{ and } x_1+x_2+\hdots+x_k=2019.