Seventeen lines and one-hundred-and-one points

  • Authors:

  • Gerhard J. Woeginger

  • Affiliations:

  • Department of Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands and Institut fur Mathematik, Technische Universitat Graz, Steyrergasse 30, A-8010 Graz, Austria

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2004

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Abstract

We investigate a curious problem from additive number theory: Given two positive integers S and Q, does there exist a sequence of positive integers that add up to S and whose squares add up to Q? We show that this problem can be solved in time polynomially bounded in the logarithms of S and Q.As a consequence, also the following question can be answered in polynomial time: For given numbers n and m, do there exist n lines in the Euclidean plane with exactly m points of intersection?