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Squares from D(–4) and D(20) Triples

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DOI: 10.4236/apm.2011.15052    2,700 Downloads   5,917 Views  
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ABSTRACT

We study the eight infinite sequences of triples of natural numbers A=(F2n+1,4F2n+3,F2n+7), B=(F2n+1,4F2n+5,F2n+7), C=(F2n+1,5F2n+1,F2n+3), D=(F2n+3,4F2n+1,F2n+3) and A=(L2n+1,4L2n+3,L2n+7), B=(L2n+1,4L2n+5,L2n+7), C=(L2n+1,5L2n+1,L2n+3), D=(L2n+3,4L2n+1,L2n+3. The sequences A,B,C and D are built from the Fibonacci numbers Fn while the sequences A, B, C and D from the Lucas numbers Ln. Each triple in the sequences A,B,C and D has the property D(-4) (i. e., adding -4 to the product of any two different components of them is a square). Similarly, each triple in the sequences A, B, C and D has the property D(20). We show some interesting properties of these sequences that give various methods how to get squares from them.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Z. Čerin, "Squares from D(–4) and D(20) Triples," Advances in Pure Mathematics, Vol. 1 No. 5, 2011, pp. 286-294. doi: 10.4236/apm.2011.15052.

References

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[6] M. Radi?, “A Definition of Determinant of Rectangular Matrix,” Glasnik Mate-maticki, Vol. 1, No. 21, 1966, pp. 17-22.

  
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