... if the vn’s arerational, when b, c, d are rational. Then, in this case, a rational periodic solution of (5. 1) may have only periods which belong to the set { 3, 4,5 , 6,7 , 8,9 ,1 0, 12} (see [4 ]). But ... condition is that tan−1H(b,0,d) = / 3, that is H(b,0,d) = 3. If c =0 andbd =0 , then limK→+∞θ(K) =3 /8,sothefirstcondition(b)ofLemma 6.17holds if H(b,0,d) = tan2(3π/ 8) = 3+2√2.Finally, point ... = 3+2√2,andifH( 0,0 ,d) =3 +2√2,then(1.2)withc = d = 0, b>0 and with c = b =0 , d>0 (and a =1 ) has IPCB.(b) If c>0 and H(b,c,d) =1 ,thenthedifference equation (1. 2) has IPCB.(c) In...