オイラーの四平方恒等式
ただし
u 1 = b 1 2 b 4 − 2 b 1 b 2 b 3 − b 2 2 b 4 , u 2 = b 1 2 b 3 + 2 b 1 b 2 b 4 − b 2 2 b 3 . {\displaystyle {\begin{aligned}u_{1}&=b_{1}^{2}b_{4}-2b_{1}b_{2}b_{3}-b_{2}^{2}b_{4},\\u_{2}&=b_{1}^{2}b_{3}+2b_{1}b_{2}b_{4}-b_{2}^{2}b_{3}.\end{aligned}}}
次の副産物にも注意しよう。
u 1 2 + u 2 2 = ( b 1 2 + b 2 2 ) 2 ( b 3 2 + b 4 2 ) . {\displaystyle u_{1}^{2}+u_{2}^{2}=(b_{1}^{2}+b_{2}^{2})^{2}(b_{3}^{2}+b_{4}^{2}).}