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Beyond Pythagoras I have been asked to investigate Pythagorean triplets where the shortest side is an odd number and all the three sides are positive integers. A pythagorean triple is a set of integers (a,b,c) that specifies the lengths of a right angle triangle a²+b²=c² in which 'a' is the shortest side 'b' is the middle side and 'c' is the hypotenuse. The first set of triples (3,4,5) which has already been proved to satisfy Pythagoras's theory. I have also been given two other pythagorean triples (5,12,13) and (7,24,25) I will now prove these to satisfy Pythagoras's theory a² = 5² =25 b² = 12² =144 c² = 13² =169 a²+b² =25+144 =169 a²+b²=c² so Pythagoras's theory holds for (5,12,13) because they satisfy the condition of a²+b²=c² in a right angled triangle. a² = 7² =49 b² = 24² =576 c² = 25² =625 a²+b² =49+576 =625 a²+b²=c² so Pythagoras's theory holds for (7,24,25) because they satisfy the...

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