Let m and n be positive integers such that m>n and m−n=1. Consider the three integers m2−n2, 2mn, and m2+n2.
a. (i) Prove that these three integers can always represent the sides of a right-angled triangle.
b. (ii) List all distinct triples produced by this relation for which the hypotenuse does not exceed 100.
c. (iii) For each triple obtained in part (ii), determine whether it is primitive and give justification for your answer.