MathDB
Lattice points within the n x n first quadrant [ILL 1977]

Source:

January 11, 2011
analytic geometrycombinatorics proposedcombinatorics

Problem Statement

Let nn be an integer greater than 11. In the Cartesian coordinate system we consider all squares with integer vertices (x,y)(x,y) such that 1≤x,y≤n1\le x,y\le n. Denote by pk (k=0,1,2,…)p_k\ (k=0,1,2,\ldots ) the number of pairs of points that are vertices of exactly kk such squares. Prove that ∑k(k−1)pk=0\sum_k(k-1)p_k=0.
Back to ProblemsView on AoPS