不定方程x^2+mxy+ny^2=z^2的一族整数解

On Integer Solutions of Indefinite Equation x^2+mxy+ny^2=z^2

讨论不定方程x2+mxy+ny2=z2满足一定条件的整数解.主要利用分解法,给出了不定方程的一族整数解.不定方程x2+mxy+ny2=z2的一族整数解为x=k(na2-b2),y=k(2ab-ma2),z=k(na2-mab+b2),式中m,n,k,a,b均为整数.

The integer solutions to an equation x2＋mxy＋ny2=z2 which satisfy some conditions are given. By using decomposition method the solutions satisfying the conditions are obtained. The integer solutions of indefinite equation x2＋mxy＋ny2=z2 are x=k（na2-b2）,y=k（2ab-ma2）,z=k（na2-mab＋b2）, where m, n, k, a and b are integers.