Investigate all right-angled triangles whose one leg has length 15 units and whose sides are integral.
a. (i) Find every pair of positive integers (b,c) such that 152+b2=c2 and list the corresponding triples in increasing order of the hypotenuse.
b. (ii) Classify each triple found in part (i) as primitive or non-primitive, giving clear reasons.
c. (iii) Prove that no other integral right-angled triangle can have a side of length 15.