**Author(s):**Zvonko Čerin

**Journal:**Advances in Pure Mathematics

ISSN 2160-0368

**Volume:**01;

**Issue:**05;

**Start page:**286;

**Date:**2011;

Original page

**Keywords:**Fibonacci Numbers | Lucas Numbers | Square | Symmetric Sum | Alternating Sum | Product | Component

**ABSTRACT**

We study the eight infinite sequences of triples of natural numbers

*A*=(

*F2n+1*,4

*F2n+3*,

*F2n+7*),

*B*=(

*F2n+1*,4

*F2n+5*,

*F2n+7*),

*C*=(

*F2n+1*,5

*F2n+1*,

*F2n+3*),

*D*=(

*F2n+3*,4

*F2n+1*,

*F2n+3*) and A=(

*L2n+1*,4

*L2n+3*,

*L2n+7*), B=(

*L2n+1*,4

*L2n+5*,

*L2n+7*), C=(

*L2n+1*,5

*L2n+1*,

*L2n+3*), D=(

*L2n+3*,4

*L2n+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.