令a=m²;+n²;b=2mn c=m²-n²
则a^2=m^4+n^4+2m²*n²
b^2=4m²*n²
c^2=m^4+n^4-2m²*n²
显然a^2-c^2=b^2
所以m²+n²; 2mn m²-n²是勾股数