关于勾股丢番图方程x^2+(x+k)~2=z^2

On the Pythagorean Diophantine Equation x^2+(x+k)~2=z^2

本文给出了勾股丢番图方程x2＋（x＋k）＝z2有正整数解的充要条件以及使该方程有正整数解k的必要条件，并根据k＝1，7时的正整数解，给出了对于给定k求该方程正整数解的一般方法。

In this paper the general recurrence forrmula of solution of pythagorean diophantine equation x2+(x+k)2=z2 is given f which contains the necessary and sufficent condition of squad whole number solution. and the squad whole number suiution k. According to the whole number solution when k=1.7. the general method of solving one saiad whole number of the equation by giving regular k is given.