MathDB

Let

N

be a positive integer. Prove that there exist three permutations

a_1,\dots,a_N

b_1,\dots,b_N

, and

c_1,\dots,c_N

1,\dots,N

such that

\left|\sqrt{a_k}+\sqrt{b_k}+\sqrt{c_k}-2\sqrt{N}\right|<2023

for every

k=1,2,\dots,N

A7