Let α and β be two real numbers such that α + β = 1 and αβ = - 1 ....

${x}^{2} - x - 1 = 0$ roots $= \alpha, \beta$

${\alpha}^{2} - \alpha - 1 = 0 ⇒ {\alpha}^{n + 1} = {\alpha}^{n} + {\alpha}^{n - 1}{\beta}^{2} - \beta - 1 = 0 ⇒ {\beta}^{n + 1} = {\beta}^{n} + {\beta}^{n - 1} + {p}_{n + 1} = {p}_{n} + {p}_{n - 1}$

$29 = {p}_{n} + 11$

${p}_{n} = 18$

${p}_{n}^{2} = 324$