Question 24
Let $P(x)$ be a polynomial with non-negative integer coefficients. A sequence of positive integers $(x_n)_{n=1}^{\infty}$ is given such that $x_1 = 1$, and for every natural number $n$, the following equality holds
$$
x_{n+1}^2 + P(n) = x_n x_{n+2}
$$
Prove that $P(x)$ would be a constant polynomial.
$$
x_{n+1}^2 + P(n) = x_n x_{n+2}
$$
Prove that $P(x)$ would be a constant polynomial.