形如n^2-n-1的Lucas数

On Lucas numbers of the form n^2-n-1

首先证明了只存在有限个 L ucas数可以表示成 n2 - n- 1的形式 ,然后证明了除 L5,L7外 ,若 L ucas数 Lm可以表示成 n2 - n- 1的形式 ,则 m必满足 m≡± 1(mod16)

The so called Lucas sequence is defined as L n+2 =L n+1 +L n,L 0=2,L 1=1 . It is well known that the Lucas characteristic equation is x 2-x-1 =0. Lucas numbers can be written as the form of the characteristic equation. First, it is proved that there are finite Lucas numbers which are the form n 2-n-1 . Then, it is proved too that if L m=n 2-n-1 , then m ≡±1 (mod 16) besides L 5 and L 7 .