Abstract:

We established a wonderful theorem about 2-partition on three circles when researching the Vander Waerden Number.Based on the theorem，we revealed a new law of quadratic residue:for prime number p，about p/4 quadratic residues or quadratic nonresidues are isolated points;in addition,about p/4 have the interval length of at least 2.

Key words: quadratic residue, distribution density, interval length, [p]_k transformation