Consider the set of positive integers that satisfy x2+y2=z2.
a. (i) Define a primitive Pythagorean triple.
b. (ii) Show, with proper reasoning, that (9,40,41) is a primitive Pythagorean triple while (15,36,39) is not.
c. (iii) Let k be a positive integer such that k(9,40,41) is again a Pythagorean triple whose perimeter does not exceed 100. Find all possible values of k and list the corresponding triples.