MathDB

15

Part of 1977 IMO Longlists

Problems(1)

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

Source:

1/11/2011
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.
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