Problem

Source: Indian TST Day 1 Problem 3

Tags: geometry, invariant, algebra unsolved, algebra



Starting with the triple (10072,20142,100714), define a sequence of triples (xn,yn,zn) by xn+1=xn(yn+znxn) yn+1=yn(zn+xnyn) zn+1=zn(xn+ynzn) for n0.Show that each of the sequences xnn0,ynn0,znn0 converges to a limit and find these limits.