Let \( \alpha \) and \( \beta \) be the roots of the equation \( x^{2}-x-1=0 \). If \( p_{k}= \) \( (\alpha)^{k}+(\beta)…

Let \( \alpha \) and \( \beta \) be the roots of the equation \( x^{2}-x-1=0 \). If \( p_{k}= \) \( (\alpha)^{k}+(\beta)^{k}, \mathrm{k} \geq 1 \), then which one of the following statements is not true?

[JEE Main 2020, 7 Jan (Shift 2)]