MathDB

6

Part of 2011 Baltic Way

Problems(1)

Number of lines through origin and precisely one other point

Source: Baltic Way 2011

11/6/2011
Let nn be a positive integer. Prove that the number of lines which go through the origin and precisely one other point with integer coordinates (x,y),0≤x,y≤n(x,y),0\le x,y\le n, is at least n24\frac{n^2}{4}.
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