Abstract:
Using modulo 5（mod 5）operation of the lattice points in the plane, 25 lattice points are arranged into a ring surface lattice with 5 row rings and 5 column rings. The ring surface is called mod 5 ring surface, marked Z25. Symmetry between lattice points, between rows, between columns, and between diagonals are discussed, respectively. Based on these symmetries,it is pointed out that the distributing law of the 5!lattice points on Z25 whose centroid on is still a lattice point. It is proved that when lattice points have different remainders after mod 5 operation, in any 9 lattice points,there exist 5 lattice points whose centroid is still a lattice point, the formula n(5)=9 found.
