A Direct Method To Generate Pythagorean Triples And Its Generalization To Pythagorean Quadruples And n-tuples

Details A Direct Method To Generate Pythagorean Triples And Its Generalization To Pythagorean Quadruples And n-tuples A Direct Method To Generate Pythagorean Triples And Its Generalization To Pythagorean Quadruples And n-tuples

2012-01-10

arxiv.org/abs/1201.2145v1

Mathematics

Number Theory

11 pages

Scientific paper

The method of generating Pythagorean triples is known for about 2000 years. Though the classical formulas produce all primitive triples they do not generate all possible triples, especially non-primitive triples. This paper presents a direct method to generate all possible triples both primitive and non-primitive for any given number. Then the technique is generalized to produce Pythagorean Quadruples and n-tuples. Our method utilizes the fact that the difference between lengths of the hypotenuse and one leg of a Pythagorean triangle can have only certain distinct values depending on the length of the other which remains true for higher tuples also.

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