(Solved):
Problem 3: Define the integer sequences (xn)n=1 and (yn)n=1 by xn+yn2=( ...
Problem 3: Define the integer sequences (xn?)n=1?? and (yn?)n=1?? by xn?+yn?2?=(3+22?)n (So x1?=3 and y1?=2. And since (3+22?)2=17+122?, we get x2?=17 and y2?=12. Etc.) Show that xn2??2yn2?=1 for all n?N.