Pythagorean triples are positive integers a, b, and c that satisfy the Pythagorean equation a2 + b2 = c2. a. Find three sets of Pythagorean triples other than 3, 4, 5. b. Prove that 3, 4, 5 is the only Pythagorean triple with consecutive integers as sides. c. Prove that no isosceles right triangles exist for which the sides are Pythagorean triples. d. Prove that in every Pythagorean triple, at least one leg is a multiple of three