二次齐次丢番图方程sum from i=1 a_ix_i^2=by^2全部整数解

The general expressions of integral solutions of the Diophantine equations _(i=1)~n∑a_ix_i^2=by^2

勾股定理(即毕达格拉斯定理)的全部整数解表达式有无穷多种,目前常用的勾股定理全部整数解表达式,不过是其中最简通解式而已。Legendre方程,二次齐次丢番图方程若有一组非全零整数解,则有无穷组整数解,并且全部整数解的表达式有无穷多种。给出其全部本原解,全部整数解的通解式。

The general expressions in integer of the Pythagorean Theorem have infinite equivalent forms. The familiar general expression in integer of the Pythagorean Theorem is just a simplest form. Legendry equation, or equation, if it has a group of integer solutions which are not all zeros, then it has infinite groups of integer solutions and it has infinite equivalent general expressions. The general expression of primitive solutions and the general expression in integer are given.