关于Evans问题的一个结果

用初等数论的思想方法研究Evans问题,可以证明：△ABC是以c为底的本原Evans三角形的充要条件是其三边由本原Heron数组公式所给出,且相应参数要满足（mt＋ns）（ms-nt）│2mnst.当本原Heron数组公式中m=s=k,n=k-1,t=k＋1（k∈N＋,k≥2）时可以得到一类本原Evans三角形.

A Result on Evans Problem

By the method of elementary number theory, this paper studies Evans problem. It is proved that a necessary and sufficient condition for /NABC being a primitive Evans triangle with c as its hemline is that the three edges are obtained by the primitive Heron array formula, and the parameters in the formula satisfy （rnt＋ns）（ms = nt） │ 2mnst. A class of the primitive Evans triangles are obtained when m= s = k, n=k-1, t = k＋l （k∈N＋, k≥2） are required in the primitive Heron array formula.