CONSTRUCTION OF IRRATIONAL GAUSSIAN DIOPHANTINE QUADRUPLES
Keywords:Diophantine quadruple, irrational Diophantine quadruples, Gaussian Diophantine quadruples, Pell equations, Double Diophantine equations, integer solutions
Given any two non-zero distinct irrational Gaussian integers such that their product added with either 1 or 4 is a perfect square, an irrational Gaussian Diophantine quadruple ( , ) a0 a1, a2, a3 such that the product of any two members of the set added with either 1 or 4 is a perfect square by employing the non-zero distinct integer solutions of the system of double Diophantine equations. The repetition of the above process leads to the generation of sequences of irrational Gaussian Diophantine quadruples with the given property.
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