For each of the following questions, begin by compiling some data; next examine the data and formulate a conjecture; and finally try to prove that your conjecture is correct. (But don’t worry if you can’t solve every part of this problem; some parts are quite difficult.)
(a) Which odd numbers a can appear in a primitive Pythagorean triple (a, b, c)?
(b) Which even numbers b can appear in a primitive Pythagorean triple (a, b, c)?
(c) Which numbers c can appear in a primitive Pythagorean triple (a, b, c)?
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