论文标题
在K将pell-lucas序列中进行完美的力量
On Perfect Powers in k-Generalized Pell-Lucas Sequence
论文作者
论文摘要
令k> = 2，让（q_ {n}^{（k）}）_ {n> = 2-k}是由k-eneralized pell序列定义的 q_ {n}^{（k）} = 2q_ {n-1}^{（k）}+q_ {n-2}^{（k）}+...+...+q_+q_ {n-k}^{（k）} for N> = 2在初始条件下 q _ { - （k-2）}^{（k）} = q _ { - （k-3）}^{（k）} = ... = ... = q _ { - { - 1}^{（k）} = 0，q_ {0} {0}^{（k）^{（k）} = 2，q_} = 2，q_ {1} {1}}^{k {k）} = 2。 在本文中，我们解决了双方方程 q_ {n}^{（k）} = y^{m}在正整数N，m，y，k中，带有m，y，k> = 2。我们表明，该方程的所有解决方案（n，m，y）在正整数n，m，y，k中，使得2 <= y <= 100均由（n，m，y）=（3,2,4），（3,4,2），k> = 3给出。也就是说，q_ {3}^{（k）} = 16 = 2^4 = 4^2 for K> = 3。
Let k>=2 and let (Q_{n}^{(k)})_{n>=2-k} be the k-generalized Pell sequence defined by Q_{n}^{(k)}=2Q_{n-1}^{(k)}+Q_{n-2}^{(k)}+...+Q_{n-k}^{(k)} for n>=2 with initial conditions Q_{-(k-2)}^{(k)}=Q_{-(k-3)}^{(k)}=...=Q_{-1}^{(k)}=0, Q_{0}^{(k)}=2,Q_{1}^{(k)}=2. In this paper, we solve the Diophantine equation Q_{n}^{(k)}=y^{m} in positive integers n,m,y,k with m,y,k>=2. We show that all solutions (n,m,y) of this equation in positive integers n,m,y,k such that 2<=y<=100 are given by (n,m,y)=(3,2,4),(3,4,2) for k>=3. Namely, Q_{3}^{(k)}=16=2^4=4^2 for k>=3.
