Question

Show that:
a) For all i = 2, ..., x, we have |t_i| < |t_i+1| and r_i-1*|t_i| < a, and that for all i = 3, ..., x, we have |s_i| < |s_i+1| and r_i-1*|s_i| < b;
b) s_i*t_i <= 0 for i = 0, ..., x + 1
c) if d := gcd(a,b) > 0, then |s_x+1| = b/d and |t_x+1| = a/d