MathDB

Easy Lattice Maximum

Source: 2022 Taiwan TST Round 2 Independent Study 2-C

April 9, 2022

combinatoricslattice points

Problem Statement

There are

2022

distinct integer points on the plane. Let

I

be the number of pairs among these points with exactly

1

unit apart. Find the maximum possible value of

I

. (Note. An integer point is a point with integer coordinates.)
Proposed by CSJL.