4

Part of 2009 Baltic Way

Problems(1)

Find n so that inequality holds

Source: Baltic Way 2009

Determine all integers

n>1

for which the inequality x_1^2\plus{}x_2^2\plus{}\ldots\plus{}x_n^2\ge(x_1\plus{}x_2\plus{}\ldots\plus{}x_{n\minus{}1})x_n holds for all real

x_1,x_2,\ldots,x_n

inequalitiesinequalities proposed