Explain the determine green and the inf is here Theorem 8. If o is even and k, 1 are odd positive integersand (A+D+ 1) + (B+ C), then Eq.(1) has no primeperiod two solution.Proof.Following the proof of Theorem 5, we deduce that ifo is even and k, 1 are odd positive integers, then x, = Xn-oand Xn+1 = xn-k= Xn=1. It follows from Eq.(1) thatbP=(A+D) Q+(B+C)P –(18)(e – d)andbQ = (A+D) P+ (B+C) Q –(19)(e – d)By subtracting (19) from (18), we get(P- Q) [(A+D+ 1) – (B+C)] = 0,Since (A+D+1) – (B+C) + 0, then P= Q. This is acontradiction. Thus, the proof is now completed.O Theorem 5.If k,1 and o are both even positive integers,then Eq. (1) has no prime period two solution.Proof.Assume that there exists distinct positive solutionsP,Q, P, Q,..of prime period two of Eq.(1). If k,1 and o are both evenpositive integers, then x, = Xp-k= Xn-1= Xn-o.from Eq. (1) thatIt followsP=(A+B+C+D) Q –(ed)(12)|andbQ= (A+B+C+D)P –(13)(e – d)'|By subtracting (13) from (12), we get(P- Q) [A+B+C+D+1]=0.||Since A+ B+C +D+1 0, then P:contradiction. Thus, the proof is now completed.OQ. This is a6.The objective of this article is to investigate somequalitative behavior of the solutions of the nonlineardifference equationbxr- k[dxn-k- exn-1](1)Xn+1Axn+ Bxn–k+ Cxn–1+Dxn-o +n = 0,1, 2, ....where the coefficients A, B, C, D, b, d, e € (0,0), whilek,1 and o are positive integers. The initial conditionsX-,..., X_1,..., X_k ….., X_1, Xo are arbitrary positive realnumbers such that k <1< 0. Note that the special casesof Eq. (1) have been studied in [1] when B=C= D=0,and k= 0,1= 1, b is replaced by – b and in [27] whenB=C= D=0, and k= 0, b is replaced by – b and in[33] when B = C = D = 0, 1= 0 and in [32] whenA=C= D=0, 1=0, b is replaced by – b.6.

Name: Explain the determine green and the inf is here Theorem 8. If o is eve
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Description: Explain the determine green and the inf is here Theorem 8. If o is even and k, 1 are odd positive integersand (A+D+ 1) + (B+ C), then Eq.(1) has no primeperiod two solution.Proof.Following the proof of Theorem 5, we deduce that ifo is even and k, 1 a