MathDB

Let

n \geqslant 3

be an integer, and let

x_1,x_2,\ldots,x_n

be real numbers in the interval

[0,1]

. Let

s=x_1+x_2+\ldots+x_n

, and assume that

s \geqslant 3

. Prove that there exist integers

i

and

j

with

1 \leqslant i<j \leqslant n

such that

2^{j-i}x_ix_j>2^{s-3}.

A4