SQUARES IN EULER TRIPLES FROM FIBONACCI AND LUCAS NUMBERS

摘要

In this paper we shall continue to study from [4], for k = -1 and k = 5, the infinite sequences of triples A = (F2n+1, F2n+3, F2n+5), B = (F2n+1, 5F2n+3, F2n+5), C = (L2n+1, L2n+3, L2n+5), D = (L2n+1, 5L2n+3, L2n+5) with the property that the product of any two different components of them increased by k are squares. The sequences A and B are built from the Fibonacci numbers Fn while the sequences C and D from the Lucas numbers Ln. We show some interesting properties of these sequences that give various methods how to get squares from them.