If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the following must be true?
I. x > z
II. x = y + z
III. y^2 + z^2 is a positive integer	Pick
A) I only B) II only C) III only D) I and II only E) I and III only
x^2 = y^2 + z^2 is the equation for the Pythagorean theorem.   I. x &gt; z -&gt; always true since hypotenuse is the longest side   II. x = y + z -&gt; never true since the length of any side of a triangle is less than the sum of length of other two sides   III. y^2 + z^2 is a positive integer -&gt; true in this case since it is given that y and z are positive integers   Answer (E).   I and III only is the correct answer
<result>E</result>
If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the following must be true?
I. x > z
II. x = y + z
III. y^2 + z^2 is a positive integer