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In this paper we introduce a formula that parameterises the Pythagoreantriples as elements of two series. With respect to the standard Euclideanformula, this parameterisation does not generate the Pythagorean triples wherethe elements of the triple are all divisible by 2. A necessary and sufficientcondition is also proposed for a Pythagorean triple obtained from this formulato be primitive.

A new parameterisation of Pythagorean triples in terms of odd and even series