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Pythagorean Triples Introduction A Pythagorean triple is a set of integers (a, b, c) that specifies the lengths of a right angle triangle, i.e. a2 + b2 = c2 in which a is the shortest side, b the middle side and c is the hypotenuse or the longest side of the right angle triangle as shown in Figure 1. The first set of triples is (3, 4, 5) because 32 + 42 = 52 The second set of triples is (5, 12, 13) because 52 + 122 = 132, the third set (7, 24, 25) because 72 + 242 = 252, and so on. Thus there are infinitely such sets of triples that exist in this way. I can tabulate some of the first few triples so that I can get my preliminary results. Preliminary Results Table 1. First five sets of Pythagorean triples Triple Number n Shortest side a Middle side b Longest side c Perimeter P Area A 1 3 4 5 12 6 2 5 12 13 30 30 3 7 24 25 56 84 4 9 40 41 90 180 5 11 60 61 132 330 In Table 1,...

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