Let {xn}n≥0 and {yn}n≥0 be two sequences defined recursively as follows x0=1,x1=4,xn+2=3xn+1−xn,y0=1,y1=2,yn+2=3yn+1−yn. [*] Prove that xn2−5yn2+4=0 for all non-negative integers. [*] Suppose that a, b are two positive integers such that a2−5b2+4=0. Prove that there exists a non-negative integer k such that a=xk and b=yk.