问题
单项选择题
If x, y, and z are positive integers and x2=y2+z2, which of the following must be true ？（）
Ⅰ.x＞z
Ⅱ.x=y+z
Ⅲ. y2+z2 is a positive integer
A. Ⅰ only
B. Ⅱ only
C. Ⅲ only
D. Ⅰ and Ⅱ only
E. Ⅰ and Ⅲ only
答案
参考答案：E
解析：
Statement Ⅰ must be true, because if all three variables are positive integers and x2=z2 plus the square of another positive integer, then x has to be greater than z;, plug in numbers to verify. Ⅲ must be true because the square of a positive integer is always a positive integer, and y2+z2 is equal to the square of a positive integer (i.e.=x2). Ⅱ does not have to be true because if you square both sides of x=y+z, you get x2=y2+2yz+z2, which does not agree with the original statement.