二次剩余定理的推广——二次剩余函数的值域

The promotion of the quadratic residue theorem——The field of the quadratic residue function

任何奇素数p有(p-1)/2个二次剩余,此就是二次剩余定理。提出二次剩余函数的概念,证明了素数模p任一二次剩余函数的值域都有(p+1)/2个元素。二次剩余定理乃是它的一种特殊情形,从而推广了二次剩余定理。

Any odd prime number P has P-1/2 quadratic residue. This is the quadratic residue theorem. The article gives the concept of the quadratic residue function, and proves a theorem that the field of any quadratic residue function of prime modulus P has P＋1/2 elements. The Quadratic Residue Theoremis a special kind of the theorem.