Question 170
A sequence $(x_n)$ is defined as follows
$$
x_0 = 2,\ x_1 = 1,\ x_{n+2} = x_{n+1} + x_n
$$
for every non-negative integer $n$.
a) For every $n \ge 1$, prove that if $x_n$ is a prime number then $n$ is a prime number or $n$ has no odd prime divisors.
b) Find all pairs of non-negative integers $(m, n)$ such that $x_m \mid x_n$.
$$
x_0 = 2,\ x_1 = 1,\ x_{n+2} = x_{n+1} + x_n
$$
for every non-negative integer $n$.
a) For every $n \ge 1$, prove that if $x_n$ is a prime number then $n$ is a prime number or $n$ has no odd prime divisors.
b) Find all pairs of non-negative integers $(m, n)$ such that $x_m \mid x_n$.