A. 510. There is given a positive integer n and some straight lines in the plane such that none of the lines passes through (0,0), and every lattice point (a,b), where 0a,bn are integers and a+b>0, is contained by at least a+b+1 of the lines. Prove that the number of the lines is at least n(n+3).
Deadline expired on 10 June 2010.