**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 0*a*,*b**n* 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).

(5 points)