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Ronald J.Evans在文[1]中提出一个未决问题:“求出所有的整数边三角形,使它的某个高与底边之比为整数.”此问题被Richard K.Guy收录在其著名的《数论中未解决的问题》一书~[2]中.Guy指出,这个比不能为1和2,但可以为3,并提出问题:这个比能否取大于3的整数?定义1某个高与底边之比为整数的整数边三角形称为Evans三角形.定义2 Evans三角形中是整数的高与底边
Ronald J. Evans proposed an open question in [1]: “Find all integer edge triangles so that its ratio of a certain height to the bottom edge is an integer.” This question has been included by Richard K. Guy. In his famous book “Unresolved Problems in Number Theory” ~[2], Guy pointed out that this ratio cannot be 1 and 2, but it can be 3, and raises the question: Can this ratio be an integer greater than 3? Definition 1 Integer edge triangle whose ratio of height to bottom is an integer is called an Evans triangle. Definition 2 The height and the bottom of an Evans triangle are integers.