Let (xn) be an integer sequence such that 0≤x0<x1≤100 and
xn+2=7xn+1−xn+280,∀n≥0.
a) Prove that if x0=2,x1=3 then for each positive integer n, the sum of divisors of the following number is divisible by 24xnxn+1+xn+1xn+2+xn+2xn+3+2018.
b) Find all pairs of numbers (x0,x1) such that xnxn+1+2019 is a perfect square for infinitely many nonnegative integer numbers n.