Abstract
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.
Highlights
CONSTRUCTION OF IRRATIONAL GAUSSIAN DIOPHANTINE QUADRUPLESGopalan*1, S.Vidhyalakshmi, N.Thiruniraiselvi3 *1Professor, Department of mathematics, Shrimathi Indira Gandhi College, Trichy, Tamilnadu, INDIA 2Professor, Department of mathematics, Shrimathi Indira Gandhi College, Trichy, Tamilnadu, INDIA 3Research Scholar, Department of mathematics, Shrimathi Indira Gandhi College, Trichy, Tamilnadu, INDIA Abstract: 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
We construct sequences of irrational Gaussian Diophantine quadruples with properties D(1) and D(4)
Summary
Gopalan*1, S.Vidhyalakshmi, N.Thiruniraiselvi3 *1Professor, Department of mathematics, Shrimathi Indira Gandhi College, Trichy, Tamilnadu, INDIA 2Professor, Department of mathematics, Shrimathi Indira Gandhi College, Trichy, Tamilnadu, INDIA 3Research Scholar, Department of mathematics, Shrimathi Indira Gandhi College, Trichy, Tamilnadu, INDIA Abstract: 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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