Combinatorics · Lattice points · Area estimates · Telescoping sums · Symmetry
Prove that the disk of radius \(100\) centred at the origin contains fewer than \(31600\) points whose two coordinates are both integers. (A point counts as contained in the disk if it lies inside it or on its boundary.)
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Serbian National Competition (Drzavno takmicenje) 2018, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source