论文标题
关于斐波那契和fibonacci数字的混合串联串联
On Mixed Concatenations of Fibonacci and Lucas Numbers Which are Fibonacci Numbers
论文作者
论文摘要
令$（f_n）_ {n \ geq 0} $和$（l_n）_ {n \ geq 0} $分别为fibonacci和lucas序列。在本文中，我们确定所有斐波那契数的斐波那契和fibonacci和卢卡斯数字的数字。通过$ a $ a和$ b $的混合串联，我们的意思是两个串联$ \ overline {ab} $和$ \ overline {ba} $一起，其中$ a $和$ b $是任何两个非负整数。 So, the mathematical formulation of this problem leads us searching the solutions of two Diophantine equations $ F_n=10^d F_m +L_k $ and $ F_n=10^d L_m+F_k $ in non-negative integers $ (n,m,k) ,$ where $ d $ denotes the number of digits of $ L_k $ and $ F_k $, respectively.我们在对数中使用线性形式的下限，并在Diophantine近似中使用减少方法来获得结果。
Let $(F_n)_{n\geq 0}$ and $(L_n)_{n\geq 0}$ be the Fibonacci and Lucas sequences, respectively. In this paper we determine all Fibonacci numbers which are mixed concatenations of a Fibonacci and a Lucas numbers. By mixed concatenations of $ a $ and $ b $, we mean the both concatenations $\overline{ab}$ and $\overline{ba}$ together, where $ a $ and $ b $ are any two non negative integers. So, the mathematical formulation of this problem leads us searching the solutions of two Diophantine equations $ F_n=10^d F_m +L_k $ and $ F_n=10^d L_m+F_k $ in non-negative integers $ (n,m,k) ,$ where $ d $ denotes the number of digits of $ L_k $ and $ F_k $, respectively. We use lower bounds for linear forms in logarithms and reduction method in Diophantine approximation to get the results.
