论文标题
在Diophantaine方程式上
On the diophantaine equations $J_N +J_M =F_A$ & $F_N +F_M =J_A$
论文作者
论文摘要
令$ \ left \ lbrace f _ {k} \ right \ rbrace_ {k \ geq0} $为$ f_ {k {k} = f_ {f-1}+f_ {k-2} $ with所有$ n \ geq2 $ with Initals $ f _ f _ fibonacci序列。 f_ {1} = 1 $。令$ \ left \ lbrace j_ {n} \ right \ rbrace_ {n \ geq0} $为$ j_n = 2J_ {n-1}+j_ {n-2} $ jacobsthal序列，用于所有$ n \ geq2 $ aints $ n \ geq2 $ with intirts $ j_0 = 0 $ j_1 = 0 $ j__1 $，$ n \ geq2 $。在本文中，我们找到了两个二磷酸方程式的所有解决方案$ j_n +j_m = f_a $，$ f_n +f_m = j_a $在非阴性整数变量（n，m，a）中，即我们确定所有fibonacci的数字，这些数字是两个jacobsii norks和jacobs的总和。
Let $\left\lbrace F_{k}\right\rbrace_{k\geq0}$ be the Fibonacci sequence defined by $F_{k}=F_{F-1}+F_{k-2}$ for all $ n\geq2$ with initials $F_{0}=0\; F_{1}=1$. Let $\left\lbrace J_{n}\right\rbrace_{n\geq0}$ be the Jacobsthal sequence defined by $J_n=2J_{n-1}+J_{n-2}$ for all $ n\geq2$ with initials $J_0=0$, $J_1=1$. In this paper we find all the solutions of the two Diophantine equations $J_n +J_m =F_a$ ,$F_n +F_m =J_a$ in the non-negative integer variables (n,m,a),i.e we determine all Fibonacci numbers which are sum of two Jacobsthal numbers, and also determine all Jacobsthal numbers which are sum of two Fibonacci numbers.
