设 m,n∈ N,m n,m与 n互素且奇偶性各异 .设 a =m2 - n2 ,b =2 mn,c=m2 + n2 ,记以 a,b,c为三边的直角三角形内的整距点个数为 f ( m,n) .文 [1 ]已得出两个重要结果 ,本文作为引理引入如下 :引理 1　在直角坐标系中 ,以 A( - n,m) ,B( anc,amc)及原点 O为顶点的 Rt△ AOB内的 Let m, n ∈ N, mn, m and n be mutually prime and have different parity. Let a = m2 - n2, b = 2 mn, c = m2 + n2, and remember that a, b, c are the three sides of the right angle The number of integer points in a triangle is f (m,n). [1] has drawn two important results. This paper is introduced as a lemma as follows: Lemma 1 in a Cartesian coordinate system, with A(-n, m) , B( anc,amc) and the origin O is the vertex within Rt △ AOB